Costa, who was reportedly involved in a training-ground bust-up last week and the subject of a mega-money offer from China, returned to the starting line-up after missing the trip to Leicester last weekend.
And he netted his 15th Chelsea goal of the season in first-half stoppage time from 12 yards after Victor Moses’ cross following a frustrating opening 45 minutes at Stamford Bridge.
Hull were no pushovers, and were denied a penalty when Marcos Alonso kicked the heel of Abel Hernandez, but Chelsea wrapped up the win on 81 minutes through Gary Cahill’s header from Cesc Fabregas’ free-kick.
The result means Arsenal are currently Chelsea’s nearest challengers, as the Blues gained points on Liverpool, Tottenham, Man City and Man Utd this weekend with 16 games remaining. Hull are 19th, two points off safety.
Title favourites Chelsea now face a decisive fortnight as they go to Liverpool on January 31, before hosting Arsenal on February 4.