Camara (right) scored his second crucial goal for Wigan in a week
Emmerson Boyce headed Wigan's winner five minutes from time to deny luckless West Brom.
Boyce's first goal in three years completed Wigan's comeback, after Henri Camara capitalised on Paul Robinson's mistake to equalise.
West Brom took a deserved lead when Ishmael Miller took advantage of Titus Bramble's error to slot home.
Wigan's hero was goalkeeper Chris Kirkland, who produced four brilliant second-half saves to deny Albion.
James Morrison made an instant contribution on his recall to the West Brom team, wriggling to the dead-ball line in the opening minute where his pull-back almost found the stretching Miller.
But the Baggies were let off the hook seven minutes later when Emile Heskey flicked on a near-post corner and Camara - rewarded for his midweek winner against Everton with a place in the starting line-up - stole in at the far post to volley over from four yards.
West Brom will feel mugged - Bruce
West Brom were happy to throw men forward and Jonathan Greening from the right, and Chris Brunt from the left, both whipped in good crosses which begged for a team-mate to attack the ball.
Greening slipped Boyce in to sprint clear but Miller's stirling effort to support his skipper was in vain as Greening lashed a poor shot high and wide.
It was then Heskey's turn to waste a good opportunity, rising to meet Luis Antonio Valencia's cross only to plant a header wide from six yards out.
West Brom certainly knocked the ball around with confidence and aplomb but their lack of ideas in the final third showed why they had only scored two league goals away from home.
Both keepers had been innocent bystanders until the 41st minute when Baggies' Scott Carson plunged low to his left to tip Ryan Taylor's curling free-kick around the post.
West Brom made the perfect start to the second half when Miller gave them the lead.
The goal had its roots deep in the West Brom penalty area where Paul Robinson dispossessed Valencia and fed Brunt to play a ball down the line.
Bramble appeared to have the situation in hand but his attempt to chest the ball down only gifted the ball to Miller, who strode on before slotting the ball past Kirkland for Albion's first goal in 344 minutes of football.
Morrison could have doubled the Baggies' lead minutes later as he broke clear, only for Kirkland to spread himself and save with his legs.
Robinson's foul on Valencia gave Taylor another sight of goal and his free-kick took paint off the outside of the post with Carson flat-footed behind his wall.
As Wigan pushed for an equaliser they left gaps at the back and Greening fed Brunt who was again denied by a fine save by Kirkland.
We had enough chances to win - Mowbray
But out of nothing, Wigan found an equaliser, with Robinson turning from hero to villain. His attempted header back to Carson was spotted by Camara who acrobatically volleyed home with his back to goal.
It then took a superb last-ditch tackle from Jonas Olsson to deny the Senegal striker a second.
Kirkland again came to Wigan's rescue, parrying Olsson's powerful header from point-blank range with Robinson firing the loose ball over the bar.
The England keeper saved his best until last, reacting to block Greening's thumping shot from 12 yards.
Wigan dashed Albion's hopes of a point with a winner five minutes from time, when Boyce was not picked up at the far post and he bulleted in a header from Jason Koumas's corner from 12 yards.
Wigan manager Steve Bruce: "We have to pay a big compliment to our goalkeeper because he has won us the game.
"We have not played particularly well but we have managed to nick a result.
"West Brom will go away from here thinking that they have been mugged. Against Middlesbrough it happened to us when we were all over them and they scored against us in the last minute.
"If you do not take your chances in the Premier League you get punished."
West Brom boss Tony Mowbray:
"We created more than enough chances to win the game but ended up losing it.
"Generally, week-in, week-out, we are better than the opposition on the balance of play but football is about being clinical in both boxes.
"We'll keep going, we have what we have, but we paid a heavy price."
Wigan: Kirkland, Taylor (Melchiot 70), Bramble, Boyce, Figueroa (Kilbane 81), Valencia, Brown (Koumas 60), Cattermole, Palacios, Heskey, Camara. Subs Not Used: Pollitt, Kingson, De Ridder, Cywka.
Goals: Camara 61, Boyce 87.
West Brom: Carson, Zuiverloon, Meite, Olsson, Robinson, Morrison (Moore 89), Koren, Greening, Borja Valero, Brunt (Bednar 89), Miller. Subs Not Used: Kiely, Cech, Barnett, Kim, Filipe Teixeira.
Booked: Miller, Greening.
Goals: Miller 47.
Att: 17,054
Referee: Phil Dowd (Staffordshire).
BBC Sport Player Rater man of the match: Wigan's Luis Antonio Valencia (8.00, on 90 minutes)
Please note that you can still give the players marks out of 10 on BBC Sport's Player Rater after the match has finished.
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