Eden Hazard put Jose Mourinho’s side ahead in the seventh minute at Stamford Bridge and Costa wrapped up the win shortly after Hull’s Tom Huddlestone had been dismissed for an ugly challenge on Filipe Luis on the hour.
The victory helped Chelsea re-assert their status as league leaders after last weekend’s defeat at Newcastle United, while defeat means Hull, who slipped to second-bottom, have now gone nine games without a win.
The mid-week Champions League victory over Sporting Lisbon had helped Mourinho’s side put the Newcastle loss behind them.
But having dropped five points in their previous three league games, the meeting with Steve Bruce’s Hull had acquired added importance for the home side.
Hull’s preparations were disturbed by growing uncertainty over the future of winger Hatem Ben Arfa, on loan from Newcastle, who has reportedly returned to his native France after falling out of favour.
With confidence low, Hull’s initial aim was to establish a foothold in the game and deny Chelsea the chance to assume early control.
Mourinho’s side, however, gave the visitors no time to settle and after completely dominating the opening exchanges, the home side took the lead.
Hull were convinced John Mikel Obi had fouled Sone Aluko in the build-up, but referee Chris Foy thought otherwise, allowing Nemanja Matic to pick out Oscar on the left wing with a threaded pass.
The Brazil playmaker moved the ball back inside onto his right foot and, spotting Hazard’s run, delivered an accurate cross towards the far post, where the Belgium international finished with a downward header.
Hull’s problems continued to mount when, three minutes later, centre-back Michael Dawson pulled up with a hamstring problem and was replaced by Alex Bruce.
– Willian, Costa dives –
The visitors’ task was now even more daunting, but having established an early advantage, Chelsea appeared to ease off.
Willian and Oscar remained busy in midfield and Branislav Ivanovic supported well on the right flank, but the home side’s display did not possess the spark required to kill off the game.
Hull attempted to force their way back into the match, but lacked the quality to make the most of the few half-chances that came their way.
Aluko was guilty of wasting their best first-half opportunity when he was sent clear on the left side of the home penalty area by Nikica Jelavic in the 21st minute, only to slice his shot wide.
Despite the lack of opportunities at either end, the game became increasingly fractious.
Foy cautioned two Chelsea players -– Willian and Costa -– for diving and ignored strong Hull complaints that Gary Cahill — who had already been booked — should have been shown a second yellow for the same offence.
Tempers eventually spilled over when Huddlestone launched into a studs-up challenge that caught Filipe Luis on the knee and earned the Hull midfielder a red card.
Now undermanned, it seemed only a matter of time before Hull’s defences were breached for a second time.
And it took Chelsea just eight more minutes to find a way through and put the game beyond the reach of the visitors.
Hazard was the creator this time, stretching Bruce’s side with a cross-field run before exchanging passes with Ivanovic and playing a reverse ball that picked out Costa’s darting run.
The striker has already shown his strengths as a ruthless finisher this season and he gave Hull goalkeeper Allan McGregor no chance with an angled, right-footed shot that crept inside the far post.