Jesse Lingard's smartly taken 61st-minute strike at a rainy Stamford Bridge had set United on course for a third straight win, which would have lifted them to within four points of the Champions League places.

But Costa equalised in the 91st minute, rounding United goalkeeper David de Gea to score and thereby extending interim manager Guus Hiddink's unbeaten run to 10 matches since he succeeded the sacked Jose Mourinho.

Mourinho's shadow continues to stalk United manager Louis van Gaal and reports that the Portuguese has been lined up to replace him are unlikely to go away after a result that left his side six points below the top four in fifth place.

Costa's goal, his seventh in nine games, gave Chelsea something to show for their efforts after an awkward afternoon that saw Kurt Zouma stretchered off with a serious-looking knee injury.

Hiddink's men remain 13th, 17 points below the top four.

John Terry was making his first home appearance since revealing that he will leave at the season's end and while he did not mention the matter in his programme notes, Chelsea's fans made their displeasure at the club's failure to offer him a new deal by chanting his name from kick-off.

Both teams were unchanged, but while Chelsea made a cautious start, United picked up where they had left off in the mid-week 3-0 win over Stoke City.

Cameron Borthwick-Jackson and Michael Carrick both dispatched long-range sighters before Thibaut Courtois was called into serious action in the 18th minute, palming Anthony Martial's drive around the post.

Chelsea were struggling to get out of their own half, but United could not maintain their initial rhythm and as the half wore on, the hosts took the upper hand.

Costa and Nemanja Matic threatened with headers, the latter obliging De Gea to leap to his right and save, while Costa drilled a shot across goal and wide from Oscar's pass.

Oscar planted a shot into the Shed End after a one-two with Cesar Azpilicueta and Willian flashed a cross across goal after leaving Borthwick-Jackson on the deck with a sharp feint.
                  
- Zouma agony -                  
                  
United flickered -- Marouane Fellaini heading wide, Matteo Darmian crossing menacingly -- before Chelsea's hands flew into the air when a shot from Terry struck Daley Blind on the elbow inside the visitors' box.

But as replays showed, the Dutchman's arm had been clamped to his chest and referee Michael Oliver waved away the penalty appeals.

United reasserted themselves after the change of ends and Courtois was obliged to parry a low shot from Wayne Rooney before Martial breezed past Branislav Ivanovic and shot wide.

Shortly after, a curling effort from Lingard drew a one-handed stop from Courtois, who sprang to his feet to shovel Rooney's drilled follow-up behind.

Seeking to give his side an attacking foothold, Hiddink introduced Eden Hazard in place of Oscar in the 54th minute, and a minute later his hand was forced again following Zouma's injury.

The 21-year-old France international screamed in agony after landing awkwardly following an aerial challenge and following four minutes' treatment he was stretchered off, with Gary Cahill coming on.

Two minutes later United added insult to injury by taking the lead, Rooney cushioning Borthwick-Jackson's cross into the path of Lingard, who took a touch before hooking home a right-foot shot on the turn.

Hiddink added Pedro Rodriguez to the mix and after De Gea had saved brilliantly from Ivanovic and Cesc Fabregas, Costa equalised.

United substitute Memphis Depay conceded possession, allowing Fabregas to slide a pass into the box, and with Borthwick-Jackson succeeding only in sliding the ball away from De Gea, Costa had the simple task of slotting into an empty net.

The Spain international might even have won it, but after taking aim from Hazard's pass, he was denied by De Gea.