In a pretty tight game, Hull had some decent spells, particularly in the first half, but badly lacked creativity and Hazard, who José Mourinho had praised in his pre-match press conference, was the decisive factor as his solo goal gave all three points to the Blues.
It was a scrappy start to the game with both sides contributing to a spell of no real chances and plenty of shoddy padding. Hull came the closest when Jake Livermore let fly from range after fine work from Yannick Sagbo to hold the ball up, but Petr Cech was able to tip it around the post.
Whether it was sluggishness, the sun in their eyes, or some unseen malaise, Chelsea appeared to be struggling and playing far too many loose passes to concede possession to the hosts. John Terry let Hull have the best chance of the game up until that point by giving the ball away cheaply in defence and presenting Sagbo with a one-on-one, but the Ivorian had to take his shot quickly under pressure from Gary Cahill and blazed a dreadful effort well wide.
Hull's defence had been robust up until that point, albeit not severely tested, but they were caught flat-footed when a loose ball slithered through to Oscar, no more than twelve yards out, dead centre of goal with a clear shot. The Brazilian blasted his effort straight down the middle of goal, but Allan McGregor somehow managed to react in a nanosecond and charge forward to tip it over the bar.
Hull managed to get to the break intact, albeit perhaps cursing their failure to score from their periods of dominance. And it soon came back to haunt them, as the Hull defence gave Hazard a ridiculous amount of space to step inside at will before lashing a shot into the bottom corner past the unsighted McGregor.
Hull were unable to keep up the intensity of pressing that they had maintained in the first half, although they did have a good spell towards the end of the half as Ahmed Elmohammady's delivery continued to be the main threat posed by the hosts, in the absence of seemingly any other source of creativity.
That allowed Chelsea to hold out without too much trouble, and Fernando Torres secured the points late on with a second goal on the break, advancing on Alex Bruce before firing low past McGregor to remove all hope for the hosts.
That leaves Chelsea in a good position with the rest of the title challengers facing some difficult tests over the rest of the weekend. It's still dull, it's still low-scoring, it's still sluggish, but José Mourinho's blue machine rumbles on.
Hull City: McGregor, Chester (Fryatt 77'), Bruce, Davies, Elmohamady, Figueroa, Meyler (Koren 67'), Huddlestone, Livermore, Boyd (Quinn 83'), Sagbo.
Chelsea: Cech; Azpilicueta, Cahill, Terry, Cole; Ramires (Essien 90'), David Luiz; Willian (Schurrle 83'), Oscar (Mikel 79'), Hazard; Torres.
Goals: Hazard 56', Torres 87'