After a dominant open period of the match, Latics were caught against the run of play by two first half goals from James Morrison and an own goal by Gary Caldwell.
Arouna Kone pulled one back almost instantly from West Brom's second but, the visitors frustrated Latics and prevented Roberto Martinez's men from battling back.
Martinez's side remained unchanged as Ben Watson kept his place from the Tottenham Hotspur game, with James McArthur still out injured.
From the off Latics looked relatively in control as they camped in West Brom's half for the opening 30 minutes.
A minute later though and they were caught out from the wings as Chris Brunt curled the ball in from the left, finding the head of Morrison who rose above Caldwell to thump his header home.
Latics' rhythm was knocked off course and around 10 minutes later West Brom made it 2-0.
The Baggies caught Latics sleeping again as they capitalised with an attacking throwing.
Billy Jones was allow to cross the ball and it cannoned off Caldwell who dove to block and into the net.
A matter of seconds later Latics had kicked off and kicked on when Jean Beausejour received the ball out wide after clever play from Franco Di Santo in the middle.
The Chilean's low cross had West Brom on the back foot and Kone arrived at the back post to tap the ball in to make it 2-1.
Latics came back out after half time with the familiar commanding style but, West Brom grew back into the game.
The second half past with rare incident as the away side set up to defend efficiently.
Latics did have a golden opportunity when Shaun Maloney lashed over the bar from close range after Di Santo's cut back but, as the West Brom defence ran out to block on the penalty spot, the Scotsman leaned back and sent the ball high.
Defeat for Latics has ended their current back-to-back win record but, the result will look harsh after an effective start to each half, with their goal also rarely threatened.