Pep Guardiola's side put themselves on the brink of title glory with Saturday's 3-1 victory at Tottenham and United's failure to take points off the bottom side on Sunday left City beyond mathematical reach. Manchester City ended their three-match losing run with a convincing win over Tottenham at Wembley Stadium.
West Brom have maintained their top-flight status for the last seven seasons but appear likely to drop to the Championship if they do not pick up wins in their five remaining matches.
On Sunday, Man United could hammer another nail in the Baggies' Premier League coffin, given their 12-point gap from safety, when the two lock horns at Old Trafford.
While letting West Brom have a feel for the game, United will have felt in control but when it came to pushing forward and punishing their opponents the home side faltered.
United's forwards were kept at bay in the first-half and Ben Foster's breathtaking save to deny Romelu Lukaku gave the Baggies real belief in the 65th minute.
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City need just nine points from their final games to set a new record for most Premier League points while another 11 goals would see them set a new goal-scoring record.
Mata sliced wide from just outside the penalty area before the ineffective Pogba was hauled off for Anthony Martial just before the hour in a desperate attempt to inject some spark into United's lifeless attack.
There were a few United half-chances before half-time, while a Dawson header back across goal from a corner was begging to be turned in by West Brom.
Manchester City would be crowned champions if the Red Devils is defeated in the game.
The City manager's decision to forego the match looked justified considering West Brom's awful form, although Jake Livermore's early attempt was a warning shot that undercooked United failed to heed.
United had to at least draw to keep the title race mathematically alive but were stunned at Old Trafford when Jay Rodriguez headed home after the break.