The Blues started slowly and almost went behind when Robert Snodgrass' deflected free-kick forced Thibaut Courtois into a diving save with just four minutes gone.
And it didn't get any better for the visitors throughout the first half, with Marcos Alonso’s wayward header proving to be their best chance.
But after the break Chelsea found their shooting boots and Eden Hazard’s 20-yard strike forced David Marshall into his first save of the day.
Chelsea almost went ahead when Costa skipped past Marshal and struck towards the goal, but the ball bounced off the post before N'Golo Kante fired the rebound over the bar.
But they took the lead soon after when Willian curled home a sublime right-footed strike from 18-yards out.
Costa then doubled the visitors' advantage soon after, firing home from inside the area to put the game out of sight for Hull.
Conte's men could have had another when Alonso found Pedro, but the Spaniard stabbed the ball wide and Hull were lucky to only conceed twice.