After a low-key first half, the game sprang into life in the second period as goals from the former Valencia man and the free-scoring Spaniard proved enough for the points
Goals from Pablo Hernandez and Michu proved to be enough for a win, despite a late surge by Roberto Martinez's men and Emmerson Boyce's strike.
The hosts started the first half like a team with a point to prove, but after their initial pressure came to nothing, Wigan were able to find themselves a foothold in the game.
Indeed, it was the Latics who had the fist real chance of the match, as the lively Arouna Kone helped Boyce's knock-down back across goal for Shaun Maloney, who hit his shot rather tamely into the grateful arms of Michel Vorm.
Michael Laudrup's choice to move Michu from his usual position in midfield to a lone striker role seemed to deny the Swans a goal-scoring dimension in their loaded midfield, with Jonathan de Guzman, Ki Sung-Yueng and Leon Britton failing to make telling runs into the Wigan box.
This meant that the home side's attackers were largely feeding off half-chances, and goal-machine Michu failed to hit the target with either a volley from the edge of the box or a header from a corner in the opening half hour.
Wigan seemed happy to soak up the pressure and hit the hosts on the counter, and again came close when Maloney found Jean Beausejour with a beautifully-weighted through ball, only for the Chilean winger to ignore Kone in the centre and blaze the ball over the bar from inside the box.
For all Swansea's energetic wing play, Michael they failed to really trouble the visitors' defence as the game petered out towards half-time.
Normal service was resumed after the break, with Swansea enjoying significant territorial dominance but unable to get too many bodies into the box.
Leon Britton got the crowd on their feet early on with a well-struck shot that went just wide of Al-Habsi's goal, and the midfielder was slightly unfortunate not to notch his first ever Premier League goal.
Swansea finally started to pile more players into the box, and were rewarded when Hernandez latched onto Wayne Routledge's pass in the penalty area before turning and firing in his first goal in English football.
The Liberty Stadium erupted, and fans barely had time to take their seats before the home team doubled their lead, as Michu grabbed his customary goal with a header from De Guzman's corner.
However, any hopes of coasting to victory were immediately dispelled as Wigan hit back straight away to halve the deficit.
A ball into the box was knocked down by the impressive Kone, and James McArthur's scuffed shot across goal was turned in acrobatically by Boyce with an audacious back-heeled volley.
Swansea were stunned, and it could have been worse moments later as Kone was controversially adjudged to be narrowly offside as he chested Beausejour's cross into the back of the net.
The game was blown wide open by that crazy five minutes, and there were chances at both ends as Wigan piled forwards in search of an equaliser and left themselves exposed to the counter attack.
However, the Swans did just enough to hold on for a valuable three points that will ease the pressure on Laudrup.