Darren Bent opened the scoring with his first Premier League goal since September after just five minutes.
But the Latics hit back thanks to a firm header from right-back Emmerson Boyce at the back post, and then they took the lead on the stroke of half-time after some calamitous defending by Villa.
Ashley Westwood's clearance off the line hit Nathan Baker and the ball rebounded into the back of the net. However, Villa rescued a point on the hour mark thanks to their skipper Ron Vlaar, who struck home a stunning volley from the edge of the box.
It was a slow start from the hosts and Ali Al Habsi, brought back into the side in place of Joel Robles, was called into action in the third minute to punch away Joe Bennett's free-kick.
With Christian Benteke suspended, Bent made his first start since January, and it only took the striker five minutes to make his mark. Paul Scharner played Bent onside and the former England man netted his first Premier League goal in nearly eight months with a shot that went in off a post.
The Latics soon levelled things up as Roger Espinoza swung over a cross from the left and Boyce leapt above Bennett to head powerfully past Brad Guzan.
Shaun Maloney forced Guzan into a decent save from a 20-yard free-kick in the 40th minute, and in stoppage-time the hosts went ahead.
Maloney's corner caused havoc in the Villa defence and, although Westwood cleared Ben Watson's shot off the line, he directed the ball against Baker, who could not stop it rolling into the net.
Wigan carried the momentum into the second half and might well have increased their lead on a number of occasions.
Boyce scored twice on the final day of last season and the defender was close to a repeat in the 59th minute as he got on the end of an Espinoza cross but his first effort was headed away from in front of the line by Bennett while his second clipped the top of the bar.
Two minutes later Villa made Wigan pay for failing to take their chances as Bennett's long free-kick was pulled down by Vlaar and then volleyed sublimely into the top corner by the centre-back.
James McArthur thought he had scored an even better goal in the 79th minute with a volley from the corner of the area but it crashed against the bar and Arouna Kone was unable to turn in the rebound.