In-form teams Everton and Wolves shared a point at Molineux although the visitors will feel aggrieved they did not come away with all three.
David Moyes's men had the best chances, with striker Louis Saha seeing his shot rebound off the crossbar before sending a close-range header over.
And the hosts' inspired keeper Marcus Hahnemann did well to deny efforts from Leon Osman and Dan Gosling.
Wolves' best effort came from Ronald Zubar, who fired wide from 10 yards.
Everton, with an outside chance of snatching the fourth Champions League spot, should have taken the lead inside the first five minutes when the energetic Osman forced a point-blank low save from the alert Hahnemann.
Midfielder Osman went close again 10 minutes later, but this time his deflected snap-shot was gobbled up by the relieved American keeper.
Wolves, who have boosted their survival chances by picking up seven points in the last three games, only came alive midway through the first half - although the endeavours of full-back Zubar and forward Kevin Doyle largely amounted to nothing.
The defensive displays of left-back Leighton Baines and captain Phil Neville at right-back were partly responsible for that and the watching England coach Fabio Capello would have been impressed with the assured performances.
McCarthy relieved to escape with draw
One man the Italian probably wishes he could include in his World Cup squad is Saha.
The wily French striker has been in superb form this season with 13 league goals and went agonisingly close to adding to the total either side of the break.
Saha's first effort was a rocket-fuelled shot from 25 yards that violently shook the Wolves crossbar and his second was a header which he powered over from six yards.
We did enough to beat Wolves - Moyes
Baines went even closer when his firmly struck 20-yard free-kick was deflected over the crossbar via the head of Doyle.
Wolves applied some pressure late on in the game, but apart from a Zubar strike, following good work on the right from Doyle, they failed to trouble the otherwise untested Tim Howard.
Everton, hoping to close the gap on their European rivals, should have snatched victory in stoppage time, but Hahnemann's save at the feet of Gosling and a superb goalline clearance from Jody Craddock to block Tim Cahill's shot, denied them the opportunity.
Wolves manager Mick McCarthy: "I'm a little bit relieved because we had to weather a fair old storm.
"Moyesie (Everton boss David Moyes) had injuries to start with but they've come good and they're as good as anything that's come down here."
McCarthy added: "We played some great football at West Ham and got a win but we're not suddenly Barcelona."
Everton boss David Moyes: "I'm disappointed we didn't take all three points because we had a host of chances.
On the injuries to Dan Gosling and Mikel Arteta: "Dan has a sore knee and it doesn't look good, while Mikel has a bit of groin strain."
90:00+5:16 The referee blows for the end of the match.
90:00+4:41 The official flags Johnny Heitinga offside. Indirect free kick taken by Marcus Hahnemann.
90:00+4:26 Corner taken by Steven Pienaar played to the near post, clearance made by Chris Iwelumo.
Correction - 90:00+3:50 Tim Cahill takes a shot. Jody Craddock manages to make a clearance. Corner from the right by-line taken by Leighton Baines,
clearance by Christophe Berra.
90:00+3:50 Shot from 6 yards by Tim Cahill. Jody Craddock makes a clearance. Inswinging corner taken by Leighton Baines, Christophe Berra
makes a clearance.
90:00+3:25 Foul by Karl Henry on Ayegbeni Yakubu, free kick awarded. Direct free kick taken by Phil Jagielka.
90:00+3:03 Steven Pienaar takes a shot. Save by Marcus Hahnemann.
90:00+0:46 Substitution Stephen Ward comes on in place of Matthew Jarvis.
90:00+0:46 Substitution (Wolverhampton) makes a substitution, with Chris Iwelumo coming on for Kevin Doyle.
90:00+0:05 Dan Gosling takes a shot. Save by Marcus Hahnemann.
89:15 Dan Gosling takes a shot. Jody Craddock gets a block in.
89:02 Dan Gosling takes a shot. Blocked by David Jones.
88:37 Corner taken short by Leighton Baines.
87:02 Substitution Jack Rodwell goes off and Diniyar Bilyaletdinov comes on.
87:02 Shot from deep inside the area by Kevin Doyle clears the crossbar.
86:47 Short corner worked by Matthew Jarvis.
Correction - 86:29 Adlene Guedioura takes a shot. Jack Rodwell gets a block in.
86:29 Adlene Guedioura produces a drilled right-footed shot from 30 yards. Jack Rodwell gets a block in.
85:12 Free kick awarded for a foul by Phil Neville on Matthew Jarvis. George Elokobi restarts play with the free kick.
82:23 Substitution (Everton) makes a substitution, with Dan Gosling coming on for Leon Osman.
82:23 Close range shot by Adlene Guedioura misses to the left of the target.
81:32 Volleyed right-footed shot by Steven Pienaar. Save by Marcus Hahnemann.
80:09 The referee blows for offside. Marcus Hahnemann restarts play with the free kick.
79:22 Foul by Jack Rodwell on Matthew Jarvis, free kick awarded. Direct free kick taken by George Elokobi.
78:24 Corner taken left-footed by Leighton Baines, Jack Rodwell has a header from inside the six-yard box and clears the crossbar.
78:10 Steven Pienaar takes a shot. Christophe Berra gets a block in.
76:06 Leon Osman has an effort at goal from just outside the box which goes wide of the left-hand upright.
75:52 Free kick awarded for a foul by Kevin Foley on Steven Pienaar. Sylvain Distin takes the direct free kick.
75:04 Substitution Louis Saha leaves the field to be replaced by Ayegbeni Yakubu.
75:04 Effort on goal by Ronald Zubar from deep inside the area goes harmlessly over the bar.
72:20 Jack Rodwell concedes a free kick for a foul on Adlene Guedioura. Marcus Hahnemann restarts play with the free kick.
71:36 Shot on goal by Kevin Foley from just inside the area clears the crossbar.
70:01 Matthew Jarvis concedes a free kick for a foul on Phil Neville. Phil Neville takes the free kick.
68:40 Free kick taken by Phil Jagielka.
68:40 Substitution Michael Mancienne leaves the field to be replaced by Adlene Guedioura.
68:40 Free kick awarded for a foul by Matthew Jarvis on Phil Jagielka.
67:01 Matthew Jarvis gives away a free kick for an unfair challenge on Phil Neville. Free kick taken by Phil Neville.
64:47 Direct free kick taken by Marcus Hahnemann.
64:47 Booking Steven Pienaar shown a yellow card.
64:35 Steven Pienaar concedes a free kick for a foul on Karl Henry.
62:48 Louis Saha gives away a free kick for an unfair challenge on Christophe Berra. Free kick taken by Marcus Hahnemann.
60:50 Kevin Foley gives away a free kick for an unfair challenge on Steven Pienaar. Leighton Baines crosses the ball in from the
60:04 Johnny Heitinga takes a shot. Comfortable save by Marcus Hahnemann.
55:58 Inswinging corner taken by Leighton Baines from the right by-line, Close range headed effort by Tim Cahill goes wide of the
54:40 Foul by Jody Craddock on Tim Cahill, free kick awarded. Leighton Baines has an effort direct from the free kick, Jody Craddock
gets a block in.
53:47 Effort on goal by Matthew Jarvis from just inside the box goes harmlessly over the target.
52:45 Kevin Doyle fouled by Johnny Heitinga, the ref awards a free kick. David Jones takes the direct free kick.
52:12 Louis Saha has a header from close range and clears the crossbar.
50:29 Kevin Doyle is flagged offside by the assistant referee. Phil Jagielka restarts play with the free kick.
49:28 Inswinging corner taken by Leighton Baines from the right by-line played to the near post, Sylvain Distin gives away a free
kick for an unfair challenge on Kevin Doyle. Marcus Hahnemann takes the free kick.
46:48 Free kick taken by Matthew Jarvis.
46:48 Booking David Jones is given a yellow card.
46:06 Free kick awarded for an unfair challenge on Ronald Zubar by Leighton Baines.
45:40 Jack Rodwell takes a shot. Save made by Marcus Hahnemann.
45:01 The referee starts the second half.
45:00+1:47 The referee blows for half time.
45:00+0:33 Unfair challenge on Kevin Doyle by Sylvain Distin results in a free kick. David Jones crosses the ball from the free kick
left-footed from right channel, save made by Tim Howard.
44:20 Jody Craddock produces a right-footed shot from inside the area that clears the bar.
43:35 Corner taken left-footed by David Jones.
43:20 Matthew Jarvis takes a shot from 12 yards. Blocked by Sylvain Distin.
42:46 Tim Cahill produces a left-footed shot from inside the area that goes over the bar.
42:02 Karl Henry gives away a free kick for an unfair challenge on Steven Pienaar. Direct free kick taken by Leighton Baines.
38:47 Tim Cahill has an effort at goal from outside the penalty box missing to the wide right of the goal.
37:08 Louis Saha has a drilled shot.
35:01 Phil Neville is caught offside. Marcus Hahnemann takes the free kick.
33:24 Kevin Doyle fouled by Phil Jagielka, the ref awards a free kick. Karl Henry restarts play with the free kick.
30:37 Leighton Baines takes the chance to get an effort at goal. Save by Marcus Hahnemann.
29:48 Matthew Jarvis gives away a free kick for an unfair challenge on Jack Rodwell. Leighton Baines takes the direct free kick.
26:13 Inswinging corner taken from the right by-line by Leighton Baines, save made by Marcus Hahnemann.
25:24 Free kick awarded for a foul by David Jones on Phil Jagielka. Phil Jagielka takes the direct free kick.
24:45 Johnny Heitinga concedes a free kick for a foul on Matthew Jarvis. Direct free kick taken by George Elokobi.
23:25 Free kick awarded for a foul by Kevin Foley on Leon Osman. Sylvain Distin takes the free kick.
20:01 George Elokobi produces a cross.
19:55 The ball is swung over by Kevin Foley.
17:57 Corner taken by Matthew Jarvis, save by Tim Howard.
15:15 Shot by Leon Osman. Save by Marcus Hahnemann.
14:40 Kevin Foley sends in a cross, Phil Neville makes a clearance.
13:11 David Jones concedes a free kick for a foul on Johnny Heitinga. Free kick taken by Phil Jagielka.
9:35 Louis Saha takes a shot. Marcus Hahnemann makes a save.
8:40 Leon Osman produces a left-footed shot from deep inside the area which goes wide of the left-hand post.
6:38 Louis Saha challenges Christophe Berra unfairly and gives away a free kick. Direct free kick taken by Jody Craddock.
5:25 Leon Osman takes a shot. Marcus Hahnemann makes a save.
5:06 Louis Saha crosses the ball, clearance made by Kevin Foley.
3:59 Michael Mancienne challenges Tim Cahill unfairly and gives away a free kick. Free kick taken by Sylvain Distin.
2:15 The ball is swung over by Kevin Foley, Matthew Jarvis has an effort at goal from close in which goes wide right of the target.
0:17 Christophe Berra concedes a free kick for a foul on Phil Jagielka. Free kick taken by Phil Jagielka.
0:00 The referee starts the match.
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