Talk of a title challenge from Frank Lampard’s side had been stifled by consecutive defeats to Everton and Wolves, slipping out of the top four while champions Liverpool pulled clear.
But victory on Monday moved the Blues back up to fifth after Abraham settled nerves at Stamford Bridge with a clinching pair in the 78th and 80th minutes.
Chelsea had endured a long night after Thiago Silva nodded them into a 10th-minute lead, with West Ham – after a double against their London rivals last term – on the front foot but unable to forge a legal opening.
An offside flag denied Declan Rice a seventh-minute opener after he ran onto Aaron Cresswell’s quick free-kick, rounded Edouard Mendy and slid in a superb finish from a tight angle.
Ben Chilwell went down just prior to that chance and soon hobbled off, but Silva swiftly lifted home spirits with a thumping header from Mason Mount’s right-wing corner.
Both sides had further goals struck off in an even first half, with Cesar Azpilicueta unable to keep play alive before Abraham netted and Jared Bowen later fouling Silva, yet there should have been no stopping Timo Werner. He aimed a tame finish straight at Lukasz Fabianski following a rapid break.
West Ham controlled the second period but failed to break Chelsea down and were caught out in an untidy fashion befitting a game short on quality.
Werner’s scuffed shot fell at the feet of Abraham, onside for a simple finish, and his second followed only 101 seconds later when the ball again dropped kindly as Fabianski leapt to block Christian Pulisic’s close-range header.
The scoreline was already harsh on West Ham and might have been weighted further in Chelsea’s favour had Werner’s woes in front of goal not continued with a blast against the crossbar from a presentable position.