Hazard underlined his increasing value to the Blues with a skilful 57th-minute effort that broke down Hull's otherwise impressive resistance before Fernando Torres made the victory safe three minutes from time.
Hazard, who cut into the box before finishing emphatically into the bottom corner, is Chelsea's top scorer with nine league goals.
Chelsea leads Arsenal by one point and Manchester City by two. Both those clubs have a game in hand on Chelsea.
Torres scored on his 200th Premier League appearance while Chelsea goalkeeper Petr Cech set a club record of 209 clean sheets.
Johnson hat trick
Elsewhere Adam Johnson scored a hat trick to move Sunderland off the bottom of the Premier League with a 4-1 victory at Fulham.
Johnson scored with a free kick in the 29th minute, grabbed a second in the 69th and converted a penalty kick five minutes from the end.
West Ham ended its miserable run by beating Cardiff 2-0 on Saturday to climb out of the relegation zone and hand Ole Gunnar Solskjaer a disappointing loss in his first Premier League game in charge.
Carlton Cole put West Ham ahead in the 42nd minute and the London club hung on with 10 men after James Tomkins was given a second yellow card in the 72nd before Mark Noble secured the victory on a counter attack in injury time.
Everton strengthened its claims for a top-four finish in the Premier League by beating Norwich 2-0 thanks to goals by Gareth Barry and Kevin Mirallas on Saturday.
Barry scored his 50th goal in England's top division with a fine strike from just outside the area in the 23rd minute, and Mirallas wrapped up the points with a curling free kick just before the hour mark.
Tottenham striker Jermain Defoe began his long goodbye at White Hart Lane with a goal as he helped Spurs to a comfortable 2-0 win over Crystal Palace.
In the later kick off Manchester United secured a vital 2-0 victory against Swansea to relieve the pressure on boss David Moyes.
After a goaless first half Moyes' men came out with an intensity missing from the first 40 minutes and outplayed their welsh opposition to score goals through Antonio Valencia and Danny Welbeck.