Phil Jagielka was sent off after 55 minutes but the hosts held on for the three points.
United lead the head-to-head 8-7, with two draws between the sides, ahead of Sunday’s clash at City’s home.
MPs on the Digital, Culture, Media and Sport (DCMS) committee have opened an inquiry into the link between playing sport and long-term brain injury.
The DCMS committee inquiry was launched on Wednesday.
The 31-year-old spent much of the first half of the season in the treatment room or on the bench following his return to Spurs on loan.
England striker Abraham has not scored in the Premier League since Boxing Day.
The Baggies are nine points behind 17th-placed Newcastle in the Premier League.
Everton take on West Brom on Thursday.
Pep Guardiola’s side are fighting on all four fronts.
City scored three late goals after being pegged back by Conor Coady’s equaliser.
Peter McCabe from the brain injury charity will appear before MPs on March 9.
The Gunners boss has been linked with a return to the club where he started his playing career.
Raphael Varane and Gareth Bale feature in Wednesday’s transfer gossip.
The result lifted quadruple-chasing City 15 points clear at the top of the Premier League.
Only four top-flight teams in Europe have had longer winning runs in all competitions than City’s current sequence