Premier League: Chelsea 2 Hull 0
Jose Mourinho's side suffered their first defeat of the season at Newcastle United last weekend, but looked back to their best early on as Eden Hazard headed them into a seventh-minute lead.
The hosts' early promise fizzled out, however, with chances few and far between for both sides for much of the encounter.
But Tom Huddlestone was given his marching orders on the hour mark for catching Filipe Luis with his studs, and Chelsea soon pounced to double their advantage – Diego Costa diverting the ball beyond goalkeeper Allan McGregor eight minutes later.
The victory sees Chelsea maintain their three-point advantage over second-placed Manchester City, while Hull - now without a win in nine -remain in the bottom three.
Chelsea reverted to a more familiar starting XI after making a number of changes for their UEFA Champions League win over Sporting Lisbon on Wednesday, and it was two of those returning stars who unlocked the visitors' defence with ease in the seventh minute.
Oscar was given time on the left wing to pick out the advancing Hazard with a precision cross, and the unchallenged Belgian rose well to power home a header.
The goal was Hazard's 65th in league football, but only his second header.
Hull – without the underperforming Hatem Ben Arfa amid reports the Frenchman's loan from Newcastle is on the verge of being terminated – were dealt a further blow when Michael Dawson was forced off through injury three minutes after Hazard's goal.
Steve Bruce's men were struggling to keep possession, and Petr Cech – making his first Premier League start of the season in place of the injured Thibaut Courtois – was a spectator for long spells, with Sone Aluko blasting over Hull's first opening after 20 minutes.
David Meyler resorted to using a hand as he looked to connect with a 25th-minute corner, earning a yellow card from referee Chris Foy.
Hull did eventually settle, limiting their hosts' attacking opportunities, but offered little going forward as Chelsea comfortably sat on their one-goal advantage.
Jake Livermore sent a low drive trickling wide of the left-hand upright as Hull looked to make a positive start to the second period, but their task got considerably tougher on the hour mark when Huddlestone was dismissed for a clumsy challenge on home left-back Filipe Luis.
James Chester's handball in the penalty area soon after went unpunished, before Chelsea made the most of their man advantage.
Hazard found Costa with a well-worked throughball, and the Spain international prodded past McGregor to put the match to bed.
Hull rarely looked like hauling themselves back into the tie in the closing 20 minutes, and the focus will now switch to ensuring their winless run does not hit double figures at home to Swansea City next weekend.