Derek McInnes twice took advantage of disarray in the Black Cats defence to give Albion an undeserved first-half lead and when Marcus Stewart scored his first Premiership goal of the season, Sunderland raised hopes of ending a club record run of ten successive defeats.
But the visitors rode their luck to end a run of seven straight losses and leave Mick McCarthy, Sunderland's third manager of the season, still searching for his first point from his five matches in charge.
"It was a tough result for us,'' said McCarthy. "We had two or three minutes of madness and it has cost us. For 25 minutes we played well and created chances but you have to score when you are doing that.
"We did not deserve to be two goals down and while I am sick at the moment, if we play like that in all our games next season, it will keep our spirits up.
"It's not a bubbly place at the moment. We have 19 points, we are bottom of the league and I have been telling players they will be freed at the end of the season.''
Albion boss Gary Megson said relegation was a bitter pill to swallow after having the club's fate sealed despite a rare away victory.
"It's been a strange afternoon,'' he said.
"Sunderland were already down and we knew the consequences. It's strange to win and find ourselves relegated.
"The ball is in our court to bounce back and for the first time in 18/19 years expectations are high and there is a battle there to be won.''
Stewart was twice denied by goalkeeper Russell Hoult and also hit the post while Mart Poom excelled on his home debut when keeping out a blistering drive from Larus Sigurdsson.
Disaster struck the home side in the 39th minute when Poom collided with central defender Talal El Karkouri and McInnes pounced on the loose ball to score with ease.
Three minutes later a 20-yard free-kick from Jason Koumas took a cruel deflection and though Poom's outstretched leg kept the ball out, McInnes was again on hand to finish off.
Stewart deservedly took advantage of a rare mistake by Hoult to force the ball over the line after the keeper had failed to hold on to Sean Thornton's drive.
Kevin Phillips had a header cleared off the line but despite a frantic finish, the Black Cats remain on course for the lowest ever haul of Premiership points.