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Ben Watson's deep cross was punched clear by Vorm but only to Roger Espinoza, whose volley crept in at the near post as Vorm tried to get back and defend the middle of his goal.
Swansea came out strongly after the interval and restored parity just five minutes into the second 45 minutes when Wayne Routledge clipped a ball over the top for right-back Angel Rangel. The Spaniard wasted no time in getting his shot in, volleying first time across Robles and in off the far post.
Michael Laudrup's side couldn't stay level for long, though, as Wigan retook the lead moments later through James McCarthy, who collected Gary Caldwell's pass, took a touch and then fizzed a shot low past Vorm.
The Latics had a golden opportunity to pull two goals clear when Kone picked out James McArthur, but he couldn't make significant contact from close range.
The end-to-end action continued and it was three goals in 10 second-half minutes soon after as Swansea pegged Wigan back once more. Itay Shechter's left-footed shot from the edge of the area took a deflection and it spun past Robles, creeping inside the Spaniard's left-hand post.
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Midway through the half Wigan were denied a third when Maloney's corner was met powerfully by the head of Caldwell, with Vorm leaping to his left to parry it away.
With 15 minutes to go it was Swansea who took advantage of some hesitant defending to lead the game for the first time.
The home side's defence failed to clear the ball properly and Pablo Hernandez picked it up on the edge of the area. A defender blocked his route to goal so instead he crossed to Dwight Tiendalli rushing in from the right. McArthur and Maloney should have cleared the ball but they made a hash of it, allowing Tiendalli to nick the ball and then mishit a shot that bounced over Robles and into the corner.
Vorm came off on a stretcher in the final 10 minutes after colliding with teammate Ben Davies in the area. That led to nine minutes of injury time in which Wigan pushed for an equaliser but the best efforts of Kone were not enough.
Defeat means that Roberto Martinez's side remain three points adrift of safety. Next up for them is the FA Cup final against Manchester City on Saturday evening.
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