It was an open game in the first half and it would be Hazard who handed Chelsea the lead from Cesar Azpilicueta's pull back in the 10th minute.
After a mistake from Thibaut Courtois, Sergio Aguero then equalised in the 26th minute. Hazard would then convert a rebound when his penalty was saved after Pedro was brought down in the box by Fernandinho.
Meanwhile, Tottenham Hotspur sensationally came from behind to beat Swansea City 3-1 in their Premier League clash at the Liberty Stadium.
Former Tottenham winger Wayne Routledge opened the scoring on 11 minutes, and after Spurs failed to break down a resolute Swans defence, it appeared as if the title-chasing side would suffer their first defeat in five Premier League matches.
But the visiting side kept plugging away and were rewarded when Deli Alli tapped home on 88 minutes.
Heung-Min Son then fired Spurs into the lead for the first time in the match in stoppage time, before Christian Eriksen secured all three points with his 94th minute strike.
Arsenal got their Champions League challenge back on track with a morale-boosting 3-0 win over West Ham at the Emirates Stadium.
Arsene Wenger's side were looking to snap a three-match winless run in the league that saw them drop out of the top four.
The east Londoners held them at the break but Mesut Ozil broke the deadlock early in the second half and Theo Walcott extended their advantage on 68 minutes before Olivier Giroud sealed the derby spoils late on.
Liverpool surrendered their lead late on as Josh King scored for Bournemouth in a game that ended 2-2 at Anfield.
Hull City scored three goals in the first-half and went on to claim a vital 4-2 victory against Middlesbrough to help them in their fight against relegation.
A spirited Southampton side came from behind to defeat in-form Crystal Palace 3-1 in Hampshire.