The game was overshadowed by injury to Hull midfielder Ryan Mason who fractured his skull in a clash of heads with Chelsea captain Gary Cahill in the first half and was taken to hospital to undergo surgery.
Costa scored shortly before halftime after wing back Victor Moses ran at the Hull defence and found the Spain striker in a crowded penalty area with his cross.
Costa missed last weekend's win at Leicester City with what Chelsea officials said was a back strain. British media reported that a row with backroom staff and a possible lucrative transfer to China were the real reasons behind his absence.
Cahill made sure of the victory when he headed home unchallenged from a Cesc Fabregas free kick in the 82nd minute.
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Hull said Mason was in a stable condition after surgery and was expected to remain in hospital for the next few days.
The win against Hull allowed Chelsea to capitalise on the failure of their closest title rivals to win at the weekend, except for Arsenal who beat Burnley 2-1 earlier on Sunday. Hull remain one place above bottom-placed Sunderland.
(Reporting by William Schomberg; Editing by Clare Fallon)
