The Ghana international’s wonderful first-half strike was enough to help the Jack Army record a crucial away win.
This gives the Wales-based side a narrow advantage ahead of the second-leg, with a place in the final up for grabs.
Swansea City will face the winner of the other semi-final match between Brentford and Bournemouth in the final of the play-offs.
“We have been here before, this time last year, and we know it is only a small lead,” Swansea manager Steve Cooper said after the game.
“It only matters if you manage it and protect it and that has to be the focus and mentality now going into Saturday.”
Ayew has been an integral part of Swansea since returning to the club two years ago after a loan spell Turkish giants Fenerbahce.
The 31-year-old, who is the skipper of Ghana’s Black Stars, has scored 15 goals in the Championship this season.