Antonio Conte’s side reached the knockout stages with a game to spare thanks to influential displays from Hazard and Willian at the Olympic Stadium that knocked Azerbaijanis Qarabag out of the competition.
Chelsea will go into their last Group C fixture against Atletico Madrid, who take on Roma at the Wanda Metropolitano later on Wednesday, on 10 points and still in with a chance of finishing top.
Hazard scored Chelsea’s first-half opener from the penalty spot after his pass to Willian provoked a foul on the Brazilian from Rashad Sadygov, who was sent off as a result.
Willian doubled Chelsea’s lead nine minutes before the interval, collecting Hazard’s deft back-heeled pass before rolling home.
Cesc Fabregas netted Chelsea’s third from the spot in the 73rd minute after another foul on Willian, and the Brazil international crashed home his second in the closing moments.
The English champions were heavily criticised after a woeful loss at Roma in their previous Champions League match, but have now won three in a row in all competitions.
“We did everything well. We should have scored more. It is easy to play with these good players,” Hazard said.
“We have a big game at Liverpool on Saturday so it was good to have a small rest. We are ready for Saturday.”
Conte had bemoaned the fixture schedule that sends Chelsea to Liverpool for a crucial Premier League game on Saturday, just 48 hours after they return to London from the 5,000 mile (8,000 kilometres) round trip to Azerbaijan.
But he still fielded a strong side, with David Luiz starting in defence for the first time since being dropped after a reported training ground row with the Blues boss following the Roma defeat.
– Michel rattles woodwork –
Conte’s side had thrashed Qarabag 6-0 in September, but they almost fell behind early on in Baku when Maksim Medvedev was allowed to advance into the area with little resistance.
Michel picked up possession and lashed a fierce shot against a post before the rebound was blazed over.
Hazard was nominally Chelsea’s central striker but the Belgian playmaker had freedom to roam and it was from a deeper position that he triggered his side’s 21st-minute opener.
Threading a pin-point pass behind the Qarabag defence, Hazard sent Willian clear on goal and the Brazil winger tumbled into the area after Sadygov grabbed at his arm.
Referee Manuel de Sousa saw enough contact to give Chelsea the penalty and sent off Sadygov.
Qarabag were furious but Hazard ignored their complaints to stroke home the spot-kick for his sixth goal in his last seven appearances.
He followed the opener with an extravagant touch to help double Chelsea’s lead in the 36th minute.
Pedro started the swaggering move with a flick into the path of Willian, who guided the ball to Hazard.
The Belgian baffled the Qarabag defence with a sublime back-heeled pass into Willian and he made no mistake with a clinical finish.
Conte’s team struck for a third time in the 73rd minute when Gara Garayev conceded a penalty with a tug on Willian.
Fabregas’s initial spot-kick was ruled out for encroachment, but the Spaniard was unflustered as he slotted home again.
Chelsea weren’t done and Willian capped the rout with a stinging strike from the edge of the area in the 85th minute.
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