Both teams had lost key personnel during the summer with Villa losing Gareth Barry to Manchester City, while Antonio Luis Valencia and Lee Cattermole had left Wigan.
The Latics have also seen a new manager installed in Martinez and they appear to have regrouped more quickly than the home side.
Wigan had wrestled the initiative from their hosts and, even before their opener, were the more threatening side.
Villa centre-back Curtis Davies got the benefit of the doubt that he had touched the ball when tackling Rodallega, who would have been clean through on goal but for the challenge.
Villa didn't deserve anything - O'Neill
N'Zogbia thought he had put the visitors ahead when he beat Villa keeper Brad Friedel with a low, angled 22-yard shot only to see his effort come back off the foot of the post.
The Midlands outfit were a side with the lethargy of pre-season still heavy in their legs and they eventually buckled.
Villa left-back Nicky Shorey could only flick a ball down Wigan's right side to Rodallega and the Colombian striker allowed the ball to bounce before sending a half-volley from the corner of the area dipping past Friedel for the first goal.
Only a goal-line clearance from James Milner after Rodallega's far-post header kept Wigan from extending their lead before Villa's restless fans were finally given a reason to hope.
Ashley Young curled a free-kick towards the top corner of the net but keeper Chris Kirkland was equal to the effort as he palmed the strike round the post.
Martinez salutes Wigan's bravery
Martinez rose to prominence during his stint at Swansea with the stylish passing football he instilled in his side.
His influence on the Wigan side was clear to see as their passing and movement was too much for a poor Villa side, epitomised by the second goal in the 56th minute.
Wigan's willing runners dragged Villa's defence out of position and allowed N'Zogbia to find Koumas, who slotted through the legs of Friedel to end a swift counter-attack.
Sidwell summed up Villa's frustration when he put a free header wide as the home side got their season off to an inauspicious start.
Wigan's over-confidence nearly cost them when a poor back-pass nearly allowed Young to score late on but Titus Bramble flung himself to deflect the strike over.
Aston Villa manager Martin O'Neill: "After the initial 15 minutes, we were second best all afternoon.
"You can analyse everything but at the end of it all I thought we looked tired, which was a wee bit of a surprise considering we've had a pretty decent pre-season.
"We've been beaten when we should have been ready to go, and it was very disappointing indeed."
Wigan boss Roberto Martinez: "I always felt that we had too many disruptions this pre-season and we knew the key to the game was going to be the first 10, 15 minutes.
"Villa put us under massive pressure and I'm proud of the players for the way they dealt with that situation.
"After that, Wigan Athletic deserved to win. It's been a big turnaround and credit should go to the players."
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