Eden Hazard, image of Chelsea's droop from champions to a tenth spot complete last season, opened the scoring at Stamford Bridge with a punishment ahead of schedule in the second half, before James Collins evened out in the 77th moment.
Costa apparently ought to have been demonstrated a second yellow card in the wake of getting West Ham goalkeeper Adrian with a late test, however he kept focused cow a sensational champ into the base left corner from 20 yards.
The wounding Spain striker's objective topped a positive night for Conte, who gave a full introduction to previous Leicester City man N'Golo Kante and saw another debutant, substitute Michy Batshuayi, set up the triumphant strike.
Be that as it may, it was an intense annihilation for West Ham director Slaven Bilic, who lost debutant Andre Ayew to an evident right thigh harm in the 34th moment.
With both administrators spending the whole match on the edge of their specialized regions, suited and motioning animatedly, the amusement was portrayed by rushed, loose football and full-blooded handling.
Kante began at the base of midfield in the main change to the Chelsea group that began last season's opening amusement — a 2-2 draw with Swansea City that gave the principal clues of the decay that was going to set in.
Bilic handled two debutants in Ayew and left-back Arthur Masuaku, however the previous was constrained into an untimely exit in the wake of harming himself pursuing the slippery Hazard.
The hosts' high guarded line anticipated West Ham bringing solitary striker Andy Carroll into the diversion and the early risks were all Chelsea's.
Branislav Ivanovic drew a recovery from Adrian at his close post, Hazard twisted a shot a foot wide after a testing run and Willian obliged Adrian to palm a plunging free-kick over the bar.
West Ham's resistance was broken two minutes into the second half after Cesar Azpilicueta ran after an endeavored freedom by Michail Antonio on the edge of the guests' container.
In trying to make amends for his mistake, Antonio succeeded just in botching into Azpilicueta from behind, obliging ref Anthony Taylor to indicate the spot.
Risk thundered the punishment into the top of the net and inside four minutes Antonio had been supplanted by Sam Byram, the previous Nottingham Forest player raging past Bilic and straight down the passage.
With West Ham offering by no assaulting danger, Chelsea kept on assaulting, Willian working Adrian with a fresh shot and John Terry heading over.
In any case, the hosts ought to have been diminished to 10 men when Costa, booked in the primary half for dispute, got Adrian with a monstrous late test as the West Ham goalkeeper faltered over a leeway.
West Ham hoped to have pulled off a raving success and-snatch with 13 minutes remaining when Chelsea neglected to clear a corner and Wales universal Collins lashed a left-foot shot past Thibaut Courtois.
Be that as it may, with full-time approaching, previous Marseille striker Batshuayi flicked on a long ball to Costa, who steadied himself before controlling a shot between Collins' legs and past Adrian's hopeless drive.