Adam Forshaw's first ever league goal sealed the points when he coolly slid home from the edge of the box after 17 minutes.
Harry Forrester cut in from the left and fed Farid El Alagui, who touched into the path of the former Everton loanee to drill home into the far corner.
But the Bees were guilty of wasteful finishing after that, with both Tony Craig and Clayton Donaldson heading over with the goal gaping.
Donaldson almost made amends when he cut in from the left, only to see his powerful drive deflected by defender Jonathan Grounds.
The Londoners almost killed the game off late on when Spurs loanee Ryan Fredericks forced a full-length save from Latics goalkeeper Dean Bouzanis, while Farid El Alagui also saw a late header cleared off the line before the visitors staged a stirring late rally, with an aerial bombardment of the home box.