The match pitched the Premier League's most feeble attack against its leakiest defence, with Wolves having notched only 17 goals all season and Wigan conceding 44.
New signing Gary Caldwell was brought in to shore up the Latics' back four but it was Wolves who had the first good opportunity.
Sylvan Ebanks-Blake has typified Wolves' lacklustre form in front of goal this season - and the out-of-sorts striker had a gilt-edged chance to open the scoring.
Nenad Milijas adeptly squeezed the ball through a crowd of defenders into Ebanks-Blake's path but the striker could only stab it wide from 10 yards out with just Chris Kirkland to beat.
Martinez relieved to get three points
Ebanks-Blake then missed another chance to score his first goal from open play all season - heading Stephen Ward's excellent cross narrowly wide at the far post.
The scare appeared to spur Wigan on, especially their top marksman Rodallega, who proceeded to undertake a one-man mission to break the deadlock.
The Colombian first stung Hahnemann's fingertips with a fierce drive that the keeper managed to steer around the post. Minutes later, he came even closer, letting rip from 25 yards and rattling the inside of Hahnemann's post.
Rodallega's best chance fell on the stroke of half-time when Stearman clumsily tugged back McCarthy and referee Howard Webb pointed to the penalty spot.
The Wolves right-back, who had been booked for a late challenge on Paul Scharner early on, was given a second yellow card and sent to the stands.
Rodallega hit his spot-kick hard and low but Hahnemann dived down to his right to expertly parry the shot - before Scharner scuffed the rebound wide.
Rodallega and Hahnemann resumed their personal duel after the break when the Colombian's shot was well held by the American - but minutes later the impressive goalkeeper was finally beaten.
N'Zogbia broke down the right and cut the ball back to Rodallega, whose shot was parried by Hahnemann straight into the path of McCarthy - and he calmly stroked the ball into the corner from 10 yards.
It was the 19-year-old Irishman's first Premier League start.
Ten-man Wolves were given a way back into the match when Webb brandished a second red card of the afternoon - Thomas receiving a second booking for a late challenge on Ward.
But any optimism for the home fans was quickly extinguished when N'Zogbia struck the visitors' second.
Wolves' defence failed to deal with a throw-in on the right-hand side and Rodallega touched the ball on to N'Zogbia, who cut inside and finished with ease.
Wolves attempted to muster a response and Chris Iwelumo forced a smart save from Kirkland - but Wigan never looked in danger of relinquishing their first win in six league matches.
There was still time for Hahnemann to deny Rodallega a final time when he foiled the forward in a one-on-one.
But while the Wolves goalkeeper came out on top in that personal tussle, his team came off second best in the afternoon's bigger battle.
Wolves boss Mick McCarthy: "The referee put a block in on David Jones which impeded him for the first goal.
"When Marcus (Hahnemann) made the save, I would have liked one of my players to have the chance to get the rebound rather than be blocked by the ref.
"But I've got no problems with the sending off - it was not the most sane thing I've seen from Richard Stearman."
Wigan boss Roberto Martinez: "We looked very dangerous on the break and created good chances in the first half.
"It looked like it might be one of those days the way their keeper played - we've had a few occasions like that.
"But instead of feeling sorry for ourselves we showed maturity - it was a complete performance."
89:22 Free kick awarded for a foul by Jordi Gomez on Kevin Doyle.
87:24 Direct free kick taken by Mario Melchiot.
87:24 Booking Kevin Doyle receives a caution.
87:18 Kevin Doyle gives away a free kick for an unfair challenge on Charles N'Zogbia.
86:28 Booking Stephen Ward booked.
86:17 Free kick awarded for an unfair challenge on Charles N'Zogbia by Stephen Ward. Mario Melchiot restarts play with the free
84:48 Andrew Surman takes a inswinging corner from the right by-line to the near post.
82:12 Kevin Foley crosses the ball, Jody Craddock takes a shot. Chris Kirkland makes a save.
81:26 Stephen Ward takes the free kick.
81:26 Substitution Andrew Surman is brought on as a substitute for Nenad Milijas.
81:26 Unfair challenge on Stephen Ward by Charles N'Zogbia results in a free kick.
81:06 Hugo Rodallega takes a shot. Save made by Marcus Hahnemann.
76:24 Jordi Gomez takes a shot. Michael Mancienne gets a block in.
74:49 Chris Iwelumo takes a shot. Save by Chris Kirkland. Nenad Milijas takes a inswinging corner.
73:32 Booking Charles N'Zogbia receives a caution.
72:29 Assist by Hugo Rodallega.
72:29 GOAL - Charles N'Zogbia:Wolverhampton 0 - 2 Wigan Charles N'Zogbia grabs a goal from deep inside the penalty box to the bottom left corner of the goal. Wolverhampton 0-2 Wigan.
69:26 Gary Caldwell restarts play with the free kick. Hugo Rodallega is ruled offside. Marcus Hahnemann takes the free kick.
69:26 Booking Caution for Karl Henry.
69:12 Free kick awarded for an unfair challenge on Jordi Gomez by Karl Henry.
66:52 Marcus Hahnemann restarts play with the free kick.
66:52 Substitution Chris Iwelumo replaces Sylvan Ebanks-Blake.
66:52 Sent off Hendry Thomas is sent off by the referee.
66:41 Free kick awarded for an unfair challenge on Stephen Ward by Hendry Thomas.
65:02 Effort on goal by Charles N'Zogbia from just inside the box goes harmlessly over the target.
63:54 Unfair challenge on Kevin Doyle by Mohamed Diame results in a free kick. Free kick taken by Kevin Foley.
62:34 Shot from just outside the box by Hugo Rodallega goes over the bar.
59:21 The assist for the goal came from Hugo Rodallega.
59:21 GOAL - James McCarthy:Wolverhampton 0 - 1 Wigan James McCarthy finds the back of the net with a goal from the edge of the area to the bottom left corner of the goal. Wolverhampton
59:19 Hugo Rodallega takes a shot. Save made by Marcus Hahnemann.
58:42 Long range effort by Nenad Milijas goes over the bar.
55:47 Kevin Doyle is caught offside. Free kick taken by Gary Caldwell.
54:20 Hugo Rodallega concedes a free kick for a foul on Karl Henry. Free kick taken by Marcus Hahnemann.
53:51 Free kick awarded for an unfair challenge on Titus Bramble by Sylvan Ebanks-Blake. Direct free kick taken by Gary Caldwell.
53:20 The referee blows for offside. Indirect free kick taken by Marcus Hahnemann.
52:53 Mohamed Diame takes a shot. Blocked by Stephen Ward. Hugo Rodallega takes a shot. Save by Marcus Hahnemann.
52:08 Unfair challenge on Mario Melchiot by Nenad Milijas results in a free kick. Gary Caldwell restarts play with the free kick.
51:28 Karl Henry gives away a free kick for an unfair challenge on Jordi Gomez. Titus Bramble takes the free kick.
50:45 Effort from the edge of the area by Hugo Rodallega goes wide of the right-hand post.
50:18 Sylvan Ebanks-Blake takes a shot. Blocked by Gary Caldwell.
46:17 Free kick taken by Chris Kirkland.
46:17 Substitution (Wigan) makes a substitution, with Jordi Gomez coming on for Paul Scharner.
46:17 Unfair challenge on Mohamed Diame by Nenad Milijas results in a free kick.
45:01 The referee blows his whistle to start the second half.
45:01 Substitution David Jones replaces Matthew Jarvis.
45:00+2:55 It is the end of the first-half.
45:00+1:07 Paul Scharner has an effort at goal from close in which goes wide right of the goal.
45:00+1:07 Power penalty taken by Hugo Rodallega saved by Marcus Hahnemann. Wolverhampton 0-0 Wigan.
45:00+1:07 Sent off Red card for Richard Stearman.
45:00+0:33 Richard Stearman challenges James McCarthy unfairly and gives away a Penalty.
43:39 Corner taken left-footed by Nenad Milijas from the right by-line to the near post, Hendry Thomas manages to make a clearance.
42:01 Sylvan Ebanks-Blake challenges Titus Bramble unfairly and gives away a free kick. Direct free kick taken by Chris Kirkland.
39:38 Kevin Foley concedes a free kick for a foul on James McCarthy. Free kick taken by Chris Kirkland.
36:58 Kevin Foley delivers the ball, Jody Craddock produces a right-footed shot from inside the six-yard box that clears the bar.
36:30 Foul by James McCarthy on Richard Stearman, free kick awarded. Nenad Milijas restarts play with the free kick.
33:56 Foul by Karl Henry on Mohamed Diame, free kick awarded. Free kick crossed by Hendry Thomas, Matthew Jarvis makes a clearance.
33:28 Long distance effort by Hugo Rodallega bounces off the post.
32:14 Unfair challenge on Kevin Doyle by Mohamed Diame results in a free kick. Free kick crossed left-footed by Nenad Milijas, save
by Chris Kirkland.
31:16 Hugo Rodallega takes a shot. Save by Marcus Hahnemann. Inswinging corner taken from the right by-line by Charles N'Zogbia,
clearance made by Kevin Foley.
29:33 Hugo Rodallega takes a shot. Marcus Hahnemann makes a save.
28:31 The referee gives a free kick against Kevin Foley for handball. Maynor Figueroa takes the direct free kick.
27:55 The ball is sent over by Stephen Ward, Header from close range by Sylvan Ebanks-Blake misses to the right of the goal.
25:52 Stephen Ward fouled by Charles N'Zogbia, the ref awards a free kick. Stephen Ward takes the direct free kick.
24:59 James McCarthy produces a left-footed shot from the edge of the area and misses to the left of the goal.
24:18 Karl Henry challenges Paul Scharner unfairly and gives away a free kick. Gary Caldwell takes the direct free kick.
21:30 Free kick awarded for an unfair challenge on Jody Craddock by Paul Scharner. Marcus Hahnemann takes the direct free kick.
19:50 Unfair challenge on Matthew Jarvis by Mario Melchiot results in a free kick. Free kick crossed right-footed by Matthew Jarvis
from left wing.
18:41 Foul by James McCarthy on Karl Henry, free kick awarded. Free kick taken by Marcus Hahnemann.
18:11 Sylvan Ebanks-Blake produces a right-footed shot from close in which goes wide of the right-hand upright.
17:36 Foul by Paul Scharner on Michael Mancienne, free kick awarded. Michael Mancienne restarts play with the free kick.
16:21 Foul by Sylvan Ebanks-Blake on Charles N'Zogbia, free kick awarded. Hendry Thomas fires a strike on goal direct from the free
kick, Marcus Hahnemann makes a save.
15:48 Inswinging corner taken left-footed by Charles N'Zogbia from the right by-line.
14:30 Charles N'Zogbia takes a shot. Save made by Marcus Hahnemann. Outswinging corner taken by James McCarthy from the left by-line
played to the near post.
14:02 James McCarthy takes a shot. Blocked by Richard Stearman.
13:13 Direct free kick taken by Marcus Hahnemann.
13:13 Booking Hendry Thomas is shown a yellow card.
12:58 Stephen Ward fouled by Hendry Thomas, the ref awards a free kick.
12:39 Maynor Figueroa takes the free kick.
12:39 Booking The referee books Richard Stearman for unsporting behaviour.
12:15 Foul by Richard Stearman on Paul Scharner, free kick awarded.
11:42 The assistant referee flags for offside against Hugo Rodallega. Indirect free kick taken by Jody Craddock.
10:42 Charles N'Zogbia takes a shot. Blocked by Jody Craddock.
9:09 The assistant referee signals for offside against Sylvan Ebanks-Blake. Indirect free kick taken by Chris Kirkland.
8:15 Kevin Foley fouled by Mohamed Diame, the ref awards a free kick. Free kick crossed left-footed by Nenad Milijas, save by Chris
6:05 Free kick awarded for an unfair challenge on Nenad Milijas by Paul Scharner. Nenad Milijas has a direct shot on goal from
the free kick, blocked by Hugo Rodallega. Matthew Jarvis decides to take a short corner.
5:44 Hugo Rodallega takes a shot. Blocked by Richard Stearman.
3:11 Unfair challenge on Kevin Foley by Mohamed Diame results in a free kick. Direct free kick taken by Kevin Foley.
2:46 Kevin Doyle delivers the ball.
1:04 Sylvan Ebanks-Blake sends in a cross.
0:00 The game kicks-off.
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