Coming into the game on the back of a humiliating FA Cup exit to Bradford, the hosts knew a victory would take them above their in-form opponents in the Premier League table.
But despite being the better side and looking the more likely to find a winner as the game went on a Santiago Vergini header in the second half was the best Poyet’s men could muster.
Sunderland, unable to find the back of the net – legitimately, at least – for the third game in a row, will point to two questionable decisions from referee Mike Jones in the first period as potentially being the difference between a much-needed win and a draw .
Mr Jones opted not to send off last man Joleon Lescott despite awarding a foul for his early challenge on Danny Graham on the advice of assistant Constantine Hatzidakis, who then raised an offside flag to deny Adam Johnson a 45th-minute opener.
Poyet had pleaded with fans to get behind the team in an open letter earlier in the week and urged his players to give the crowd something to shout about and the game was just five minutes old when Cattermole played striker Graham in behind Lescott.
Graham looked to be clear, but he went to ground as the defender recovered, and the home supporters were on their feet calling for blood as the flag went up.
Jones produced only a yellow card and replays suggested there had been little contact, but there was a tangible sense of injustice as Sebastian Larsson curled the resulting free-kick into the side-netting.
The half unfolded in unspectacular fashion thereafter, with Lee Cattermole adding steel and opposite number Darren Fletcher probing for the Baggies, although with little success.
James Morrison curled an eighth-minute shot on the turn into goalkeeper Costel Pantilimon’s arms, but that was the Romanian’s only notable action of the opening 45 minutes.
Baggies midfielder Claudio Yacob was perhaps fortunate to escape without further action when he was lectured by the referee for pushing Defoe to the ground inside the penalty area for the second time while the pair awaited delivery of a corner.
However, that was not the end of the controversy as the home side were denied what they felt was a perfectly good goal on the stroke of half-time.
Ricky Alvarez crossed from the right to the far post, where Johnson controlled before rounding Ben Foster and stabbing home, only for a harsh offside flag to end his celebrations.
Larsson forced a diving save from Foster deep into injury time, but the stalemate remained.
Sunderland resumed where they had left off after the break, dominating possession, however West Brom’s organisation left little space to exploit.
Full-back Chris Brunt had to block a 55th-minute Alvarez drive after the Argentina international cut inside on to his left foot, and Craig Dawson had to be equally determined to repel Defoe’s effort six minutes later.
The home side should have gone ahead from the resulting corner when full-back Vergini met Larsson’s cross unopposed, but he glanced his header wide of the far post.
As the game entered its final quarter, Poyet sent strikers Connor Wickham and Steven Fletcher on for Graham and Alvarez, and Wickham very nearly made a swift impact when he saw Foster bundle away his header from Johnson’s 76th-minute corner, and that was as good as it got as the last push fell short.
Sunderland: Pantilimon (6), Vergini (6), O’Shea (7), Brown (8), Reveillere (6), Alvarez (6), Cattermole (7), Larsson (8), Johnson (7), Graham (6), Defoe (6).
Subs: Fletcher (6), Wickham (6), van Aanolt (5).
West Brom: Foster (6), Dawson (6), McAuley (6), Lescott (6), Brunt (7), Morrison (5), Fletcher (6), Yacob (6), Gardner (6), Berahino (5), Ideye (5)
Subs: Baird (5), McManaman (5).
Man of the match: Seb Larsson