Two goals in the final 10 minutes secured a first win as Sunderland boss for Chris Coleman and helped leapfrog fellow strugglers Burton in the Sky Bet Championship table.
Substitute James Vaughan's close-range header and a second goal from George Honeyman were enough to secure a first league win since August for the Wearsiders.
Albion had looked set for a draw that would have been more than deserved on the balance of play but instead their inability to convert chances when on top resulted in a sixth straight home league defeat, dropping them to 23rd in the table.
Clear-cut chances were few and far between in a tightly-contested first half but it was Albion who arguably shaded it.
Lucas Akins rose highest in the sixth minute to head a Matty Palmer corner over the top and skipper Luke Murphy fired a deflected effort wide of Robbin Ruiter's post with the keeper wrong-footed before Sunderland began to settle into the game.
Bryan Oviedo proved to be a useful outlet for the Black Cats down their left, a low fizzing cross into the six-yard box eventually hacked clear by Albion's Tom Naylor.
Callum McManaman fired into the side netting via a deflection before Albion finished the half the stronger, Joe Sbarra lifting a close-range effort over and Marvin Sordell fizzing a low first-time shot just wide or Ruiter's right-hand post.
Will Miller chipped a measured effort just over the bar early in the second half before Sunderland stepped up a gear and went close themselves.
Firstly, Aiden McGeady's header back across goal failed to find a blue shirt before McManaman picked out Lewis Grabban, whose effort was saved by the legs of Albion keeper Stephen Bywater.
As the wintry conditions started to play their part it was Sunderland who began to look the more comfortable with their quick counter-attacks. The Burton defence, however, stood firm and Albion were close to the opening goal again when Sordell hooked a left-foot effort onto the roof of the net after defender Ben Turner had risen highest at the back post.
But Vaughan broke the deadlock on 84 minutes when he pounced inside the six-yard box to stoop and head home a corner that had been helped on by Lee Cattermole.
And any chance the Brewers had of getting back on level terms evaporated four minutes later as another substitute, Joel Asoro, was allowed time to pick out a cross and Honeyman fired home.