Gary Breen's seventh minute header had looked good enough for long periods to settle a dour and intense encounter so vital to the survival chances of both clubs.
But the Baggies stuck to their task and, in the third minute of injury time, Zoltan Gera headed home from substitute Diomansy Kamara's left-wing corner to the dismay of the home fans so desperate for that elusive first victory.
It was no more than Bryan Robson's side deserved as Sunderland, despite showing a vast improvement on previous performances, thanks mainly to the midfield drive from former Strasbourg skipper Christian Bassila.
The Black Cats had chances to build on a dream start and leave the visitors with a mountain to climb but they gradually took over to take full advantage of a home side struggling to make any impact in the top flight.
Hopes were high, however, after a promising start. Tommy Miller's shot was deflected behind, and from Dean Whitehead's corner, skipper Breen left goalkeeper Chris Kirkland helpless with a firm header into the top corner of the net.
Three minutes later Julio Arca and Whitehead failed to connect cleanly from perfect chances and then Breen was at full stretch to meet a Whitehead free-kick.
Kirkland produced a fine diving save from Whitehead but gradually West Brom forced their way back into contention by taking a firm grip in midfield.
Alan Stubbs cut out a dangerous centre from Steve Watson at the expense of a corner from which the visitors missed the best chance of the match. Robert Earnshaw swapped passes with Watson only for Jonathan Greening at the far post to scoop his shot high and wide.
Breen twice fouled Kevin Campbell in dangerous positions, Earnshaw blasting the first against the defensive wall and Neil Clement blasting the second just too high.
Earnshaw went clear just before the break from a clever flick on and missed another great chance to send the team level at the break.
Sunderland were forced to replace the injured Miller in the 53rd minute and four minutes later manager Mick McCarthy hauled off an ineffective Stephen Elliott in an attempt to exert more pressure and steady the ship.
Arca curled a great effort just wide but the points should have been made safe in the 69th minute. Kirkland made a great stop from Whitehead only for Andy Gray to pass up the chance to force the loose ball home.
Kelvin Davis saved well from substitute Nathan Ellington in the 89th minute and with time running out, the Baggies surged forward in a last-ditch effort to salvage a point.
Justin Hoyte headed a Watson effort off the line but from the resultant corner kick from Kamara, Gera sent a header just inside the post to the delight of the West Brom fans behind the goal and to the dismay of the home supporters.
There was no hiding place for McCarthy and his under-pressure side with a crescendo of booing ringing load and clear as the dejected players trooped from the field.
McCarthy has pin-pointed a target of ten victories for Premiership survival, but failure to overcome a side that only avoided relegation on the last day of last season does not bode well for the future.
MAN OF THE MATCH: Christian Bassila (Sunderland) - The former Strasbourg captain became an instant hit with Sunderland fans on his home debut. A firm tackler and sound distribution gave the home side much needed stability in midfield before he ran out of steam in the later stages.