The Latics, who tackle Manchester City in the FA Cup final on Saturday, twice led against the Capital One Cup winners but were made to pay a heavy price from some woeful defending which leaves them three points from safety with just two games left to play.
Roger Espinoza and James McCarthy found the net for the hosts, but Roberto Martinez's former club responded on each occasion to level through Angel Rangel and Itay Schechter, before Tiendalli opened his account for the Swans with the crucial winner 14 minutes from time.
Wigan could have found themselves a goal down with just three minutes gone when stand-in left-back Espinoza's attempted pass to Paul Scharner only succeeded in releasing Wayne Routledge, who forced goalkeeper Joel to push his near-post drive behind.
Swansea were presented with another opportunity when Joel inexplicably picked up Gary Caldwell's back-pass, but Ashley Williams blazed the resulting free-kick hopelessly high over the bar, much to the amusement of the home supporters.
The deadlock was broken just before the interval as Vorm could only fist away a hanging high cross and Espinoza volleyed home from inside the box, threading his shot beyond Garry Monk, Williams and the keeper.
Wigan's lead lasted just five minutes into the second period as Swansea started strongly and deservedly drew level when Rangel volleyed home with aplomb via the base of the post after Routledge's neat ball into the box.
The home side responded immediately and in style, as Caldwell's neat through-ball released McCarthy, who burst beyond the Swansea defence to fire confidently beyond Vorm, with James McArthur then passing up a glorious chance to make it 3-1 when he failed to get a clean contact to Arouna Kone's cross six yards out.
But Caldwell was guilty of squandering possession in his own half, as Schecter was allowed two bites of the cherry and his eventual shot found the back of Joel's net after deflecting off Emmerson Boyce and clipping the inside of the post in the 59th minute.
Vorm produced an outstanding save to keep the scores level, plunging to his left to push away Caldwell's powerful close-range header after Maloney's corner, with Wigan then culpable in their own downfall 14 minutes from time.
Tiendalli was gifted the opportunity to put his side ahead as McArthur and Maloney both failed to deal with Pablo Hernandez's cross to the far post and the Dutch defender slotted beyond Joel from close range.
Swansea goalkeeper Vorm was stretchered off in a neck brace five minutes from time after a sickening collision with Ben Davies, as Wigan were unable to find a leveller despite nine minutes of added time.
Wigan boss Martinez, who revealed after the match that he feared Ronnie Stam had suffered a broken leg, admitted they paid the price for errors in defence.
He told Sky Sports: "We have so many injuries at the back and today that showed too much. We conceded sloppy goals with bad decisions. That is very unfortunate because you could see the effort of the players and the commitment and desire in wanting to win the game."
Swansea counterpart Michael Laudrup saluted the resilience of his side as they twice came from behind to take all three points.
He added on Sky Sports: "It wasn't a great football game, technically speaking, because there was too much at stake for Wigan. I think coming back twice in an away game to Wigan like this, I can be very, very pleased."