Gylfi Sigurdsson's well-taken double either side of the interval was enough to secure a deserved triumph for Swansea, who even managed to survive the last half-hour with 10-men following the dismissal of Nathan Dyer.
It means Wigan have now gone 12 matches without a win at home, a record that will almost certainly condemn them to the Championship after seven years with the big boys if they cannot change it.
Stuart Pearce was a surprise guest, having spurned the counter attraction at Manchester City to run the rule over potential candidates for England, England Under-21, Olympics and every other job he seems to be doing at the moment.
Until his early departure, Dyer impressed most, charging on to Sigurdsson's defence-splitting pass before bringing an excellent low save out of Ali Al Habsi.
Dyer then turned provider in much the same way as Sigurdsson had done to set up Scott Sinclair.
He skipped round Al Habsi, then turned the ball goalwards, only for James McCarthy to dash back and bundle off the line.
Earlier, Sinclair had rasped a half-volley wide as Swansea enjoyed their usual dominance of possession and it must have been with some incredulity that the visitors approached the break still level.
After all, Wigan had created very little.
Franco di Santo appeared to duck under a teasing cross from Jean Beausejour when all it needed was a firm touch to find the net.
Emmerson Boyce brought a decent low save out of returning keeper Michel Vorm.
There was little else for the home fans to enthuse about, so it was no surprise boos rang out at the half-time whistle, by which time Sigurdsson had struck.
Sensing Wigan had momentarily fallen asleep as the seconds ticked down to the break, Sigurdsson took his chance, curling a shot into the top corner that gave Al Habsi no hope of keeping it out.
Martinez opted to make a double change at the break, introducing Victor Moses and Mohamed Diame in a bid to get some extra attacking invention from his side.
Far too quickly though, they found themselves two adrift after Moses tripped Dyer just outside the box.
In fact, Sigurdsson found himself in roughly the same position as the one he had previously scored from - and he promptly did exactly the same thing.
It was a hammer blow for Wigan and it was difficult to see a way back into the contest for them.
Dyer provided it. Whatever his ability, needless tackles will get him into trouble.
On another day, referee Andre Marriner may not have felt his high tackle on Jordi Gomez warranted a red card. After all, it was not particularly dangerous.
This time around, Dyer saw red and Swansea were left to battle on a man down for the final half hour.
Through Diame, Moses and Di Santo, Wigan tried to pressure their opponents into mistakes.
Swansea are learning fast, though. They refused to lunge in and when Wigan prepared to take a corner, Sinclair even managed to waste time - and spark a melee - by claiming an injury the hosts clearly did not feel existed.
It certainly appears that the visitors' top-flight future is far more assured than Wigan's, who if they cannot win matches like this must wonder how they expect to collect the points required to preserve their status.
With nine minutes remaining, substitute Hugo Rodallega brought an excellent save out of Vorm.
But the hosts created little after that and they are now in big trouble.