A brace from Marc-Antoine Fortune and a Chris Brunt effort breathed new life into the Baggies' bid to beat the drop.
Tony Mowbray's side went into the Hawthorns fixture knowing that a win was essential to preserve their top-flight status and a defeat to the Latics could have sealed their fate.
The hosts started in usual fashion displaying their brand of high-tempo football and they were rewarded for their efforts when Marc-Antoine Fortune prodded home on eight minutes.
The Baggies' woeful defending this campaign may cost them come the season-finish and a rash foul resulted in Hugo Rodallega scoring his first goal in English football with a deflected free-kick on 17 minutes.
With the scores level at half-time, the Albion got themselves back in front when Chris Brunt netted from the rebound of his missed penalty before Fortune put the match to bed in the 73rd minute.
The win, the Baggies' second in three matches, lifts them to 31 points and just three from safety.
However, their goal difference is currently inferior to Hull's and it may yet require four points from their final two matches, which includes the visit of Liverpool, to pull off the another 'Great Escape'.
ContrastIf there is a growing belief at the Hawthorns, whereas the opposite is happening at Wigan.
Their problem since the turn of the year has been scoring goals and that lack of confidence showed early on.
Rodallega volleyed wide and Antonio Valencia opted to pass rather than shoot with only goalkeeper Dean Kiely - in for the injured Scott Carson - to beat.
They were made to pay in the eighth minute when Brunt's square pass into the penalty area caught out the visiting defence, allowing Gianni Zuiverloon to shoot.
Chris Kirkland did well to parry but succeeded in only diverting it up in the air where the unmarked Fortune gratefully headed home.
It was Kirkland's last action as he went off injured moments later to be replaced by Richard Kingson.
By contrast, West Brom's second-string goalkeeper made a brilliant triple save at a Wigan corner when he blocked Charles N'Zogbia's first shot, saved Paul Scharner's rebound and turned N'Zogbia's close-range follow-up around the post.
It was not long before Kingson was in the game, however, palming Menseguez's shot wide after the on-loan Argentine had put Titus Bramble on his backside with a neat turn in the penalty area.
EqualiserWest Brom were to regret missing that chance as, in the 17th minute, Rodallega finally ended his 11-match goal drought since signing in January.
The Colombia striker's 25-yard free-kick took a significant deflection off Brunt in the wall to wrong-foot Kiely, who could not keep the ball out despite his desperate efforts on the line.
Rodallega visibly grew in confidence and a driving 30-yard diagonal run from the halfway line ended with a fierce strike which just dipped over the crossbar.
Undeterred West Brom continued to push forward and Shelton Martis headed Jonathan Greening's 32nd-minute corner wide after beating Kingson to the ball while Fortune denied first by a perfectly-timed Scharner tackle and then by Kingson at his near post.
Valencia should have put the visitors ahead in stoppage time when he ran through on goal after nicking the ball off Jonas Olsson but he shot straight at Kiely.
Kiely came to West Brom's rescue eight minutes into the second half when he saved Mario Melchiot's toe-poke from Valencia's cut-back.
However, he could only watch as Scharner's angled left-foot shot from the resulting corner rolled agonisingly wide of the far post.
With matches running out West Brom knew they had to go for victory and Greening, after somehow running unchallenged from the halfway line, forced a good save out of Kingson when he should have scored.
LifelineSuch incidents often make the difference between staying up and going down but West Brom were gifted the lifeline they needed in the 59th minute.
Fortune had turned Maynor Figueroa close to the touchline but appeared to be going nowhere when Bramble clipped him and referee Peter Walton pointed to the spot.
Kingson guessed correctly and saved Brunt's spot-kick but was powerless to prevent the West Brom midfielder smashing home the rebound.
Fortune's second in the 73rd minute made the points safe for the Baggies.
Borja Valero broke down the right and pulled the ball back to the striker and he controlled, did just enough to shift Melchiot to give him a sight of goal and fired low into the bottom corner.
As if things could not get any worse for Wigan, Zaki was carried off on a stretcher with a knee injury just nine minutes after coming on as a substitute.
For the Latics the season cannot end soon enough but a rejuvenated West Brom want it to go on just a little longer.
West Bromwich Albion
1st Half Goals
Shots on Target
Shots off Target