Jose Mourinho's side dominated proceedings but were once again lifeless in attack as they had to settle for a draw for the eighth time in 15 home matches in the top flight this season.
Captain Wayne Rooney was fit enough to return to the bench but United, who were again missing Zlatan Ibrahimovic through suspension, offered little invention in the final third against a West Brom side who sat back and frustrated the hosts in impressive fashion.
Anthony Martial missed the only good chance of the first half and Henrikh Mkhitaryan was denied twice after the break, but Tony Pulis' side - 3-1 winners over Arsenal last time out - rarely looked overly stretched despite having less than 25 per cent of the ball.
The hosts kept up the pressure late on but failed to produce a moment of inspiration to break the deadlock in their first of nine matches in what promises to be a gruelling April, and goalkeeper David de Gea almost handed the visitors a goal in the dying minutes to compound their frustrations.
Come on @ManUtd we need a goal— Peter Schmeichel (@Pschmeichel1) April 1, 2017
United had 77 per cent of the possession in the opening 15 minutes but failed to carve out any sort of half-chance against a West Brom side eager to pack as many players as possible into their defensive third.
Jesse Lingard and Martial were causing some problems with runs infield and the duo combined to create what should have been the opener, with Martial heading wide from six yards out after being picked out at the far post by the England winger's cross from the right.
United were looking bereft of ideas in attack as West Brom continued to repel their advances with ease, although it took a timely challenge from Craig Dawson to deny Martial a clear run at goal following a quick exchange with Mkhitaryan just after the break.
The home fans were growing restless and it almost got worse in the 50th minute, when former United man Darren Fletcher shot against Eric Bailly in the box following a rare foray forward from the visitors.
United responded with their best move of the match, Lingard and Rashford combining to send Mkhitaryan into the area, but Chris Brunt made a crucial sliding challenge to deny him a shot before Marouane Fellaini put the rebound wide.
West Brom had barely put a foot wrong in defence throughout but, when Mkhitaryan capitalised on a rare error from Gareth McAuley, Ben Foster raced out to block the Armenia international's effort.
Foster thwarted his old club again with a fine one-handed save from a Rashford thunderbolt from 25 yards, as Mourinho introduced record goalscorer Rooney in the hope of finding a late winner.
Fletcher nearly snatched all three points on his old stomping ground as De Gea fumbled his shot from the edge of the area against the crossbar, but it was another ex-United man in Foster who ensured a share of the spoils late on when he clawed Rashford's dipping free-kick away from the top corner in acrobatic fashion.
Key Opta stats:
- This is now Jose Mourinho’s longest unbeaten run in the Premier League (W10 D9) since October 2005 (40 games with Chelsea).
- The first shot on target in this match came in the 67th minute by Henrikh Mkhitaryan.
- United in total had 18 shots but only three were on target in this match, while West Brom had just three shots in total (one on target).
- Manchester United have drawn 0-0 at home eight times in the Premier League since Sir Alex Ferguson left in 2013. There were no goalless draws at home in the four years prior to that.
- West Brom have failed to score in four of their last six league games at Old Trafford.
- However, the Baggies are just the second team in all competitions to stop Manchester United from scoring at Old Trafford this season, along with Burnley.
- Only Thibaut Courtois (13) has kept more clean sheets than David de Gea in the Premier League this season (11).