The Baggies surrendered the lead on two occasions at the Hawthorns as the ever-threatening Callum McManaman and Shaun Maloney combined to secure the win with a late goal.
The game got off to a slow start before each net was rippled within the space of 10 minutes, Shane Long putting the home side ahead before Arouna Kone leveled things up. Gareth McAuley put the Baggies back in front soon after the break but, once more, back came the visiting team as James McArthur netted another equalizer.
There was more late drama as Shaun Maloney expertly set up Callum McManaman for a dramatic late winner that keeps Roberto Martinez's men in with a decent chance of survival.
Billy Jones, Youssouf Mulumbu and Markus Rosenberg came in for Steven Reid, James Morrison and the suspended Marc-Antoine Fortune in three Baggies changes from their 3-0 win over Southampton. The Latics, meanwhile, made two changes from the draw with Tottenham as Ben Watson and Ronnie Stam replaced Maynor Figueroa and James McArthur.
The first real opening came after 10 minutes when Graham Dorrans fired a low free kick underneath the wall, after Ben Watson was penalized for handball, however the effort was tame and Joel was able to claim it with ease.
A Paul Scharner intervention stopped Baggies attacker Long from getting on the end of a fine cross from Rosenberg, before Wigan forward Kone then forced Ben Foster into a smart save with a decent long-range strike, with chances very hard to come by in the opening 25 minutes.
However with just about half-an-hour played the home side took the lead, with each prong of the attacking trio involved. Romelu Lukaku threaded Rosenberg in behind with a fantastic early ball before the forward found Long with an equally superb low cross, leaving the Irishman to tap home.
The lead didn't last long, though. Kone leveled the scores just 10 minutes later with a well-placed header back across goal, and out of Foster's reach, after an inch-perfect cross from Jean Beausejour.
With five minutes played in the second half all Wigan's good work was undone. Kone's effectiveness in the air was less impressive as he lost Baggies defender McAuley who headed past Joel following Dorrans' delivery.
Wigan refused to give up, though, with substitute McArthur coming on and making an almost instant impact as he got on the end of a in-swinging Maloney cross to head the visiting side back level.
The match swayed one way and then the other, without either side really creating any chances, before the Latics completed their amazing comeback with 10 minutes left. Maloney maneuvered his way through the Baggies defense before cutting the ball back for McManaman who tapped home after a clever run.
Joel made a fine late save to deny Dorrans before Ridgewell headed just over the bar as Wigan just about held on to the vital victory, with McManaman also clearing from the line right at the death.