Eden Hazard scored from the spot as the Blues dominated much of the match until James Collins netted a stunning equaliser against the run of play.
But with Conte looking increasingly annoyed, Costa was played through and held his nerve to beat Adrian in the 89th minute.
After a poor first half, Chelsea took the lead thanks to Michail Antonio’s clumsy challenge on Cesar Azpilicueta inside the area.
Hazard stepped up to beat Adrian with his fifth goal in his last six league games.
The Blues were the better side for much of the game until Slaven Bilic brought on Dimitri Payet, who fired a free-kick into the wall.
From the resultant corner, Collins brought down the ball and rifled home a left-footed volley to stun the hosts.
Costa was fortunate not to see red in the other major talking point as he clattered into Hammers stopper Adrian when already on a yellow.
And the controversial Spaniard arrived at the death to power home a strike that will infuriate the Hammers.
CESC FABREGAS must answer a few long, hard questions now after becoming the fall guy for new £30 million midfielder N’Golo Kante in Antonio Conte’s first game as Chelsea boss. The Spaniard was dumped on the bench.
DESPITE this there was only one change in Chelsea’s line up on the pitch anyway from the opening game last season against Swansea – Kante for Fabregas. And the manager of course with Jose Mourinho now gone.
- CHELSEA sent out their own welcome to new manager Conte from the top tier of the Matthew Harding Stand with thousands of shiny, foil mini-flags to make up a giant mosaic of the Italian tricolore.
BUT it went a bit too far as is the norm for modern over-hyped football as the teams were greeted for a routine match with over-the-top flame throwers on the touchline on an already hot evening. Ridiculous.
CONTE made the sign of the cross as ref Anthony Taylor blew his whistle for kick off. Whether it’s religion of his opinion of his team we’ll leave up to you. He also wore extremely shiny shoes.
- THE managers showed the most measured use of the ball all night when Conte volleyed a stray goal kick straight to Slaven Bilic who controlled it and looked for a quick one-two bringing a big smile from his Italian adversary.
NOT EVERY West Ham fan is ‘en-hammered’ with the lofty ambition of their club moving to a new stadium and trying to emulate the elite teams. One traditionalist banner in the away end at Stamford Bridge read: ‘Be Careful What You Wish For’. There was also a small ‘Italian Irons’ flag to make a point towards Conte.
- EDEN HAZARD showed brief but encouraging glimpses that he is regaining his zip and confidence, running West Ham ragged on a couple of occasions with his trademark dribbling runs.
HAZARD’S goal in the first game of the season last night is in stark contrast to last season when he had to wait until April 23 for his first in the Premier League.
JAMES COLLINS’S 77th minute equaliser was only West Ham’s second attempt at goal such was Chelsea’s domination of the ball.
- DIEGO COSTA was lucky not to be sent off for scraping his boot down the inside of Adrian’s right lower leg in the second half when challenging one-on-one for the ball. He had already been booked and went on to score the winner.
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