Anthony Le Tallec's 71st-minute shot was deflected home by Albion defender Steve Watson.
But Sunderland's travelling army of 4,000 fans were not bothered how the ball went in as they have waited since the victory at Middlesbrough on September 25 to see their team win in the Premiership.
Mick McCarthy's side, who had picked up just one point from the last 39, were well worth the win for their efforts in the second-half.
They took the game to Albion after the break, having struggled to make any kind of impact in the opening period, and were rewarded handsomely for their efforts.
But it was a costly defeat for Albion who had the lion's share of possession and more chances but failed to make them count.
Considering Albion knew before the game that a win would move them six points clear of the relegation zone, their start was pedestrian to say the least.
It took them fully 25 minutes to force the Sunderland goalkeeper Kelvin Davis into a save.
Davis had to pull a stop right out of the top drawer to keep Sunderland on level terms when Ronnie Wallwork whipped in a drive from 20 yards.
Wallwork's shot took a deflection off Albion midfielder Junichi Inamoto on its way towards goal and Davis did well to dive low to his right to turn the ball around the post.
That sparked Albion into a spell of pressure that saw Darren Carter fire a 25 yard free-kick just over the bar and Nathan Ellington see his close-range drive fly just too high after a knock-down by Watson.
But Albion struggled to make any real headway against the hard-working Sunderland central defenders Gary Breen and Stephen Caldwell, despite Ellington and his strike partner Kevin Campbell toiling hard.
While Albion were frustrated in attack, Sunderland offered even less up front in the opening period with strikers Jonathan Stead and Le Tallec virtual spectators.
It was left to the industrious midfielder Tommy Miller to carry the visitors' main threat as he headed and then shot wide in the final 10 minutes of the half.
That served as an inspiration at the start of the second period for Sunderland and they should really have stunned Albion by taking a 49th-minute lead.
Stead whipped in a right-wing cross that flew across the face of goal and into the path of the on-rushing Julio Arca. It looked easier to hit the target than miss, but Arca somehow managed to push his shot wide from less than six yards with the Albion goalkeeper Tomasz Kuszczak well beaten.
It was a warning that Albion failed to heed and they paid the ultimate price 19 minutes from time when Le Tallec made a surging run forward.
He was released by Liam Lawrence who won a tussle for the ball on the halfway line with Carter. Le Tallec homed in on goal, pursued by Paul Robinson and Watson.
He managed to get in a shot that was deflected off Watson and past the stranded Kuszczak to send Sunderland's travelling fans into ecstasy.