Time and again Roberto Martinez's men have ended the season strongly to stay up, but going into today's meeting five points shy of the rest, they looked in trouble.
That situation increased when Shane Long tucked in Markus Rosenberg's cross for the Baggies, but Arouna Kone levelled before the break.
Gareth McAuley put West Brom ahead again five minutes after the restart but Wigan, never-say-die merchants, equalised through James McArthur (58) and won it when Callum McManaman scored with 10 minutes left.
Wigan now have 35 points, three less than Norwich whose dismal 2013 continued as they were beaten 2-1 by Aston Villa.
Gabriel Agbonlahor scored both goals for the visitors, who ensured Paul Lambert enjoyed a happy return to his old club.
Grant Holt scored a penalty inbetween times, but Norwich are now in trouble, compared to Villa whose two wins in a week have pushed them out to 40 points.
A 0-0 draw at West Ham leaves Newcastle in bother on 38 points, but being already relegated played into the hands of Reading who went goal crazy at Fulham, winning 4-2.
Hal Robson-Kanu's early penalty put the Royals on their way to giving Nigel Adkins his first win in charge, with the Wales international doubling his tally (62).
Bryan Ruiz gave Fulham a lifeline eight minutes later but Adam Le Fondre replied and, even though Ruiz scored again (77), Jem Karacan wrapped things up for Reading.
There was no such drama at Swansea, though, as the Capital One Cup winners played out a meek goalless draw with Manchester City.
Tottenham struck a potentially lethal blow in the race for a top-four place
Spurs were struggling to find a way past Southampton at White Hart Lane until the man of the moment, PFA Player of the Year Gareth Bale, unleashed a stinging 20-yard winner to put them temporarily into fourth ahead of Arsenal, with the Gunners taking on QPR in the late game.
Tottenham's place in the top four was soon gone, though, with Theo Walcott's first-minute goal giving Arsenal a 1-0 win over QPR at Loftus Road.
Saturday's Premier League Results
Sunday's Premier League Fixtures
Liverpool vs Everton
Man United vs Chelsea
Monday's Premier League Fixture
Sunderland vs Stoke