Roberto Martinez's side lurched closer to the Championship after his former club came from behind twice to leave the Latics three points shy of safety with two games left to play
Roger Espinoza put the Latics ahead with an excellent volley on the stroke of half-time, but was outdone by Angel Rangel just after the break as the Spaniard equalised for Swansea. James McCarthy gave Roberto Martinez's troops hope of securing a crucial victory by restoring the home side's lead with a composed finish.
But a spirited comeback from Michael Laudrup's men saw Itay Shechter's looped effort restore parity before a suicidal defensive mistake allowed Tiendalli to stab home the crucial goal and leave the Latics with a mountain to climb if they are to remain in the Premier League.
Martinez made three changes to the side that beat West Brom on Saturday, with Espinoza replacing the injured Jean Beausejour, while captain Gary Caldwell and James McArthur came in at the expense of Ronnie Stam and Jordi Gomez.
Laudrup also decided to tinker with the Swansea line-up, handing a rare start to captain Gary Monk, while Tiendalli and Schechter also came in, with Chico Flores and Nathan Dyer dropping out alongside top scorer Michu, who was not even on the bench.
With the weekend's results having been favourable to Wigan, Martinez knew a win against his former employers in their long-awaited game in hand would see the club leapfrog Newcastle and Norwich out of the bottom three on goal difference. Defeat, on the other hand, was unthinkable.
However, they almost fell behind in the third minute when Wayne Routledge caught Espinoza on his heels, but could only fire into the side netting when through on goal.
Ashley Williams then scooped an indirect free-kick over the bar from eight-yards, after Joel Robles had picked up Caldwell’s nervous back-pass in Swansea’s best chance of the half.
It proved a pivotal miss as Wigan deservedly broke the deadlock on the stroke of half -time as Espinoza, showing superb technique, squeezed a first-time volley in at the near post following Vorm’s miscued punch.
But any momentum gained from taking the lead wasn’t carried over after the interval and Wigan lost the lead within four minutes of the interval. Routledge’s elegant lofted pass picked out Rangel, who’s controlled volley across goal clipped the far post before going in.
But Wigan’s recent revival has been underpinned by a mean fighting spirit and they equalised almost immediately as Caldwell’s pass split the visiting defence to find McCarthy and the midfielder finished expertly across Vorm.
Shooting themselves in the foot is another of the Latics' quirks, and just moments after McArthur squandered a golden opportunity to make it 3-1 they were pegged back once again when Shechter, anonymous otherwise, saw his snap shot deflect past the despairing dive of Robles.
With a point not good enough to shift them to a position of safety Wigan upped the ante and were only prevented from taking the lead for a third time by Vorm’s stunning point-blank save to keep out Caldwell’s bullet header.
And the consequences were duly felt with 15 minutes remaining as a catastrophic mix-up in the six-yard area allowed Tiendalli to sneak in unannounced and poke the ball home to put Swansea in front for the first time.
A sickening clash between Vorm and team-mate Ben Davies saw the Swansea goalkeeper stretchered off after lengthy treatment that offered Wigan the opportunity to regroup. But even with nine minutes of added time the Latics still came up short, and now need a miracle to avoid relegation.