Cristiano Ronaldo scored his 17th Premier League goal of the season to instantly reply to Marcos Alonso's opener but Manchester United's 1-1 draw with Chelsea dealt a heavy blow to their top-four prospects.
Chelsea dominated the first half, producing 11 shots, but David De Gea stood firm, denying Kai Havertz in their best chance.
Alonso put the visitors ahead on the hour-mark with a fine volley from eight yards after Havertz had flicked on Reece James' cross.
Ronaldo struck less than two minutes later, when he controlled a Nemanja Matic pass and drove the ball home.
The Blues pushed on in the second half and James might have won it late on, but his curling effort struck the far post.
The point leaves United in sixth place on 55 points, five behind fourth-placed Arsenal with three matches remaining, having played two matches more than the Gunners.
Chelsea lie third, with 66 points.
See: Man Utd report | Chelsea report
Next fixtures
Man Utd: 2 May v Brentford (H)
Chelsea: 1 May v Everton (A)
Match officials
Referee: Mike Dean. Assistants: Ian Hussin, Darren Cann. Fourth official: Robert Jones. VAR: John Brooks. Assistant VAR: Timothy Wood.
