Swansea had an excellent chance to take an early lead when Wigan goalkeeper Joel Robles picked up Gary Caldwell's backpass, allowing the visitors an eight-yard indirect free kick. Jonathan de Guzman touched it to centre-back Ashley Williams, but he blazed it well over the crossbar.
Kone again tested Vorm in the 26th minute, collecting a pass from Callum McManaman and drilling low from the right of the area straight at the Dutchman's legs.
Wigan were the side seeing more of the ball and, with four minutes left of the half, Shaun Maloney won a free kick 25 yards out. The Scot stepped up to take it himself and although he got it up and over the wall, Vorm was there to catch it.
It looked as if the match would go in level at the break until Espinoza's strike in the first and only minute of added time. Ben Watson's deep cross was punched clear by Vorm but only to the Honduran, whose volley crept in at the near post as Vorm tried to get back and defend the middle of his goal.
As it stands, Wigan will hop above Newcastle and Norwich, with the former dropping into the bottom three.