Thiago Silva had opened the scoring early on with a thumping header, after Declan Rice had had a sharply-taken effort ruled out for offside.
The Blues were lacklustre for much of the evening, but Abraham doubled the lead on 78 minutes and then again soon after to ensure the Blues bounced back to winning ways after successive league defeats.
It looked as if Rice had given the visitors the perfect start as he was slipped in by a quickly-taken free-kick and rounded Edouard Mendy to score but the linesman’s flag was raised and VAR confirmed the decision was just about correct.
The Blues, already without the injured Reece James, lost Ben Chilwell early on after an awkward ankle twist, but Silva lifted spirits moments later as he took advantage of some woeful marking to head home.
Jarrod Bowen was a tad unlucky to have a leveller chalked off for a foul on the Brazilian defender and the game remained in the balance until Abraham’s late double.
First, the Englishman reacted sharply to steer home after Timo Werner’s mis-hit shot turned into a perfect through-ball, and he then sealed the win by sweeping home the rebound after Lukasz Fabianski had denied Christian Pulisic from close range.
Werner might have added a fourth late on to lift a poor individual performance but the German rattled the bar after being slipped in by N’Golo Kante.