Hazard scored in the early minutes and set up Diego Costa for Chelsea’s second goal just after the hour, a goal that came not long after Tom Huddlestone had been sent off in a game that frequently threatened to boil over.
Hull’s players were upset with referee Chris Foy on more than one occasion, but he had little option but to dismiss Huddlestone for a nasty challenge that ended any chance the visitors had of taking advantage of a Chelsea display that rarely reached a level above subdued when it was 11-a-side.
Chelsea, beaten by Newcastle last weekend to end their unbeaten start to the season, were keen to get Branislav Ivanovic involved down the right flank in the early minutes, but it was a move down the left that cut a swathe through Hull’s defence for the seventh-minute opener.
Jon Obi Mikel and the impressive Nemanja Matic worked hard to win the ball in midfield and the latter fed Oscar, whose cross was perfectly placed between two static Hull defenders for Hazard to head past Allan McGregor.
Hull lost Michael Dawson soon after to an apparent hamstring injury, but they grew into the game and Sone Aluko fired over the bar with their first decent chance after Mikel had lost the ball cheaply.
Brave defending from James Chester denied Costa a chance and Gary Cahill headed way over the bar as Chelsea tried to grab hold of the game back after a quiet spell.
Cahill was lucky to escape more serious censure than a yellow card after going in over the top on Aluko, with Nikica Jelavic only able to hit the Chelsea wall with the resulting free-kick from a dangerous spot.
Hull started the second period brightly, with the Blues still strangely subdued going forward, and Jake Livermore was not far off target with a snap-shot from just outside the box.
Visiting players were again surrounding Foy on 52 minutes when Cahill appeared to take a dive in the box – his claims for a penalty were waved away but there were no further sanctions taken against the England centre-half.
The tetchiness continued as Alex Bruce was booked for a foul on Willian, and what seemed an inevitable sending-off arrived just before the hour when Huddlestone went in late on Filipe Luis and was rightly dismissed for what eventually turned into a stamp on the Spaniard’s ankle.
Chelsea were soon on the front foot and made it 2-0 on 68 minutes, with Hazard at the centre of things again as he linked up with Ivanovic and then played a cute through-ball for Costa to fire across McGregor into the net.
Any attacking instinct Hull had before the dismissal disappeared after it, and Chelsea were happy to play the ball around, with Jose Mourinho bringing on Andre Schurrle, Didier Drogba and Ramires for a run-out off the bench.
Substitute Robbie Brady had a free-kick deflected over the bar, but that was about all Hull could offer as Chelsea cruised to their eighth straight home win of the season.
The points also took Jose Mourinho to 400 Premier League points in his 174th game – he has reached the landmark 17 games quicker than previous record holder Sir Alex Ferguson and 34 quicker than Arsene Wenger.
Chelsea: Cech (6), Ivanovic (7), Filipe Luis (7), Terry (6), Cahill (6), Mikel (7), Matic (7), Willian (6), Oscar (6), Hazard (8), Costa (7).
Subs: Ramires (6), Schurrle (6), Drogba (6).
Hull City: McGregor (6), Elmohamady (5), Chester (6), Dawson (6), Davies (5), Robertson (6), Livermore (6), Huddlestone (4), Meyler (5), Jelavic (5), Aluko (7).
Subs: Bruce (5), Brady (6), Ramirez (5).
Man of the match: Eden Hazard.