Jesse Lingard’s goal looked to have earned United a first win over Chelsea since October 2012, but Costa capitalised on Daley Blind’s stoppage-time error to tuck in his seventh goal in nine games in the 1-1 Premier League draw.
The result extended the Blues’ current unbeaten run to 11 games. Guus Hiddink remains undefeated as Chelsea caretaker boss, with the Premier League champions’ most recent loss at Leicester under Jose Mourinho on Dec. 14.
Mourinho has been repeatedly linked with succeeding Louis van Gaal at Manchester United and the visiting Dutch boss would have been disappointed to see the lead lost.
United had been on course to move within 10 points of leaders Leicester and four points of second-placed Manchester City, but now Van Gaal’s men are 12 and six points behind those two, respectively.
Chelsea — and John Terry, in particular — felt they should have been ahead before Lingard’s goal.
The Chelsea captain believed Blind handled his shot in the box late in the first half and that the Blues should have had a penalty. Referee Michael Oliver disagreed.
The Blues, who lost Kurt Zouma to what appeared to be a serious knee injury, had opportunities, only for David De Gea to keep out Branislav Ivanovic’s volley and Cesc Fabregas’ near-post effort before Costa’s leveller.
Terry was making his first appearance at Stamford Bridge since last Sunday’s declaration from the skipper that Chelsea would not be renewing his contract when it expires at the end of the season.
The Blues maintain the possibility remains an offer will be tabled to the skipper, but, in a show of solidarity from the supporters, banners were peeled back from The Shed and Matthew Harding Ends, with one remaining. “JT Captain, Leader, Legend” it read.
Owner Roman Abramovich was present to hear the pro-Terry chants of “Sign him up.” Terry thanked the fans at the final whistle.
Both sides were unchanged from their midweek fixtures and United, buoyed by their 3-0 defeat of Stoke, hemmed Chelsea back for much of the opening 25 minutes.
A Michael Carrick shot extended Thibaut Courtois before Anthony Martial cut in from the left, shot viciously across goal, only for the goalkeeper to save smartly.
Chelsea belatedly responded, with a Costa header deflected narrowly wide and a Nemanja Matic header saved by De Gea.
Oscar next played in Costa, who shot wide across goal, before the playmaker blasted off target.
Willian then left Cameron Borthwick-Jackson on his bottom on the right, but his cross was out of Oscar’s reach.
United had chances too. Marouane Fellaini headed Blind’s corner just wide and Matteo Darmian’s cross was tantalisingly out of Rooney’s reach.
Chelsea’s handball appeal was dismissed and United resumed the stronger. After Wayne Rooney forced a save from Courtois, Martial ran at Ivanovic and fired just wide.
Courtois saved from Lingard, then Rooney, before Chelsea suffered a double blow. Zouma was forced off after landing awkwardly and then Lingard scored.
Borthwick-Jackson crossed from the left, Rooney laid the ball off and Lingard held off Azpilicueta to shoot high into the net.
De Gea denied Ivanovic and Fabregas before Blind was caught ball-watching and slipped as he tried to change direction, allowing Costa in.
United withstood a late bombardment from Chelsea, but it would have been of little consolation after they missed out on victory.