United kicked off proceedings without Wayne Rooney, who was resigned to the bench, but it was Javier Hernandez who got things rolling in the 5th minute when he tapped home from close range after Baggies keeper Scott Carson failed to hold on to a Nani free-kick.
The home side went two ahead 20 minutes later through Nani who played a crafty one-two with Dimitar Berbatov before snapping home into the corner.
Five minutes after the break, West Brom grafted one back in bizarre fashion when Chris Brunt's set-piece was deflected off Anderson and then Patrice Evra before whizzing past a helpless Edwin van der Sar at the near post.
The comeback was then complete when Somen Tchoyi managed an easy tap-in after van der Sar made a glaring error where he dropped a Brunt cross - his mistake costing his side all three points as they failed to bridge the gap with leaders Chelsea who drew at Aston Villa.
West Brom are the first team to take points off United at Old Trafford and the draw allowed them to remain sixth.
Venue: Old Trafford, Manchester Crowd: 75,272 Referee: Michael Jones Yellow cards:MU - Darron Gibson 58' WBA - Nicky Shorey 39', Scott Carson 80'
MU Edwin van der Sar (gk), Nemanja Vidic, Rio Ferdinand, Patrice Evra, Rafael, Anderson (Rooney 72'), Michael Carrick (Scholes 72'), Ryan Giggs (Gibson 43'), Nani, Javier Hernandez, Dimitar Berbatov
WBA Scott Carson (gk), Jonas Olsson, Gabriel Tamas, Nicky Shorey, Gonzalo Jara, Youssuf Mulumbu, Paul Scharner, James Morrison (Dorrans 86'), Chris Brunt, Somen Tchoyi (Thomas 69'), Marc-Antoine Fortune (Bednar 79')