The Gunners beat Burnley 2-1 at the Emirates where the real drama came in injury time when each side scored a penalty and Arsene Wenger clashed with the fourth official after being sent off for disputing the first spot-kick.
By contrast, the day's other game seemed routine, with Southampton beating the ailing champions Leicester City 3-0.
Chelsea are odds-on to succeed Claudio Ranieri's side as victors in May after posting their eighth successive home league win against a Hull side which had Ryan Mason taken to hospital after a sickening clash of heads with Gary Cahill.
The stage was set perfectly for the returning Costa to make more headlines after being said by the club to be missing with injury against Leicester last week while British media reported he was unsettled by the prospect of a big-money move to China.
Manager Antonio Conte said before the game that he had been happy with Costa's mentality and he will have been even more pleased with the goal that put the Blues ahead in first-half injury time after good work on the right by Victor Moses.