Albion boss Bryan Robson was forced to make a tactical reshuffle after central defender Darren Moore was sent off just before the break.
He sent on Martin Albrechtsen and sacrificed the goalscoring threat of ex-Wigan favourite Nathan Ellington.
But the switch produced unexpected dividends as the Danish defender conjured up the winner and left Wigan to reflect on their third consecutive Premiership defeat.
He got the goal but Albion had another hero in Tomasz Kuszczak who produced a series of stunning saves.
Fresh from the Carling Cup semi-final first leg win over Arsenal, Wigan had been looking for their first ever Premiership double having beaten the Baggies 2-1 at The Hawthorns in September.
With Paul Jewell so far frustrated in his attempts to strengthen his injury-hit squad, he was again restricted in his team selection with David Connolly and Steve McMillan the latest additions to the casualty list.
But Austrian defender Paul Scharner - an instant match-winning hit after coming off the bench against the Gunners - made the starting line-up for his Premiership debut.
West Brom too had their problems injury-wise with Kanu and Neil Clement among the absentees and they were aiming to avoid a third successive league defeat after losing to Villa and Liverpool before the FA Cup draw against Reading last week.
Ellington, who scored 59 goals in 130 appearances for the Latics and twice helped them to win promotion, faced his old team-mates hoping to end a seven-match barren run.
The first threat came from Albion after Ellington had forced Arjan de Zeeuw to concede a corner.
Jonathan Greening picked out Steve Watson at the back post but his powerful volley was pushed round the post by Mike Pollitt.
Jason Roberts, up against his old club, was unable to work the space to get in a shot after a clever free-kick from Jimmy Bullard, and twice Wigan failed to find the target as Scharner and Roberts both tried their luck.
Ellington thundered a shot against the crossbar but was clearly offside, and the Baggies were fortunate to survive a handball appeal against Moore after a flick-on from Scharner.
Ronnie Wallwork, booked for a foul on Leighton Baines, was fortunate not to see red after bringing down Roberts. It gave Wigan a free-kick in a good position but Bullard's shot flew straight into the keeper's arms.
The Latics had a similar opportunity when Moore fouled Lee McCulloch but Graham Kavanagh's attempt failed to trouble Kuszczak.
Hesitation by Stephane Henchoz almost proved fatal when he allowed Kevin Campbell to nip in as Albion began to give the Wigan defence a thorough examination. Wigan's luck was in though as the ball skimmed off Pollitt's head for a corner.
The impressive Scharner , operating in midfield, then tested Kuszczak with a fierce shot - Wigan's best attempt of the first half.
Then disaster struck for the Baggies when Moore was sent off after collecting his second booking of the game. Roberts flicked the ball past him, and the big defender was guilty of a cynical foul leaving referee Martin Atkinson with no option.
Manager Robson was left seething at Moore's moment of madness as Roberts was around 60 yards away from the Albion goal when the foul was committed.
Campbell was left to battle on alone up front but he still proved a handful, forcing Pollitt into desperate action after Wallwork provided a terrific cross into the danger area.
Then, against the odds, West Brom grabbed the lead. Wallwork cashed in on a slip by Scharner to send Albrechtsen racing into the area. The right-back's finish was perfection, blasting past Pollitt from the edge of the six-yard area as the keeper came out.
The Latics almost levelled when Bullard's corner was nodded back inside by Pascal Chimbonda and McCulloch's header came back off the bar.
Wigan piled on the pressure in an increasingly desperate bid to salvage a point but Wallwork cleared off the line from Chimbonda and other attempts from Bullard and Roberts flew wide of the target.
The Latics were almost caught on the break when Albrechtsen raced in on goal, forcing another save from Pollitt.
With five minutes left, Kuszczak came to the rescue again, tipping a Kavanagh free-kick round the post to deny Wigan a share of the points.
And in stoppage time, the Albion keeper came up with an outstanding save to keep out a close-range shot from Roberts when the Wigan striker seemed certain to score.
Wigan Star Man: Graham Kavanagh - A typically non-stop performance by the Irishman, Wigan's driving force in midfield. He came close to grabbing a late equaliser for Paul Jewell's men.
West Brom Star Man: Tomasz Kuszczak - The Polish keeper was simply outstanding protecting the Albion lead with some stunning saves - the best in stoppage time from Jason Roberts.