Gus Poyet's team had the better of things at the Stadium of Light but were frustrated by a stubborn defence that were set up well by Tony Pulis
The home side believed Joleon Lescott should have been sent-off early on for bringing down Danny Graham, but the defender escaped with just a yellow card.
Gus Poyet's team had much the better of things though they were unable to create any chances of note as the match ended in stalemate.
Sunderland made five changes to the side that was dumped out of the FA Cup by Bradford City last time out, with Gus Poyet drafting Lee Cattermole – out since December with niggling groin injuries – straight back into the starting line-up.
The game started in controversial fashion when referee Mike Jones deemed that Lescott had not prevented a goal-scoring opportunity when he hauled down Graham on the edge of the area.
Despite Sunderland's protestations, Lescott escaped with just a booking, while Sebastian Larsson fired into the side-netting from the resulting free-kick.
Poyet's side continued to press West Brom, with the visitors unable to get the ball into the feet of in-form striker Brown Ideye.
However Sunderland lacked the quality to make their possession count against a typically organised Tony Pulis defence, though Jermain Defoe did go close before John O'Shea headed wide from a whipped Larsson free-kick.
Adam Johnson had the ball in the back of the net in the 45th minute when, after latching onto Santiago Vergini's cross at the back post, but the strike was incorrectly disallowed for offside.
Ben Foster had to be alert again a minute later to palm away Larsson's stinging drive before the break, but Vergini could not work the England man from close range 15 minutes into the second half unmarked from Larsson's corner.
Poyet introduced Steven Fletcher and Connor Wickham with just over 20 minutes of normal time remaining, while Pulis sent on Chris Baird to shore up his defence.
Wickham brought Foster into action as Sunderland pushed for a winner, but the game ended goalless, to widespread indifference from the Stadium of Light crowd.