Rodallega pounced in the 76th minute after Marton Fulop had been at his best to repel a constant tide of home attacks.
Despite losing 9-1 at Tottenham last weekend , Wigan dominated from start to finish against a woeful Black Cats side that have now won just once away in their last 17 Premier League games.
Paul Scharner, who grabbed Wigan's goal in their 9-1 drubbing at Tottenham last weekend, tested Fulop with an early long-range strike.
Wigan were on top for the opening stages and, after Charles N'Zogbia broke down the wing and crossed, Rodallega shot into the side-netting.
Jason Scotland thought he had put the hosts ahead just before the half-hour after N'Zogbia, playing on the right flank, fired in a wicked cross that the Trinidad & Tobago international poked onto the post.
Sunderland struggled to impose themselves in the first half but they could have taken the lead four minutes after the break when Andy Reid's corner sparked panic in the Wigan box and Mario Melchiot was forced to block Phil Bardsley's shot.
At the other end Fulop was soon back in action, first blocking Titus Bramble's strike before saving from Jordi Gomez.
But after surviving for 76 minutes Sunderland finally went behind when Rodallega broke free from his man and slotted past Fulop.
The Hungarian goalkeeper had to be at his best again five minutes later to prevent Rodallega grabbing his second of the game.
Sunderland pushed forward late on but by then the game was almost up and Wigan held on to complete a remarkable turnaround from last weekend.