Eden Hazard, Cesc Fabregas and a double from Willian sealed the three points for Antonio Conte's side in Baku and ensure they will progress to the knockout phase of the competition.
Qarabag, thrashed 6-0 in the reverse fixture at Stamford Bridge in September, started well in front of their noisy home support but were left facing a huge challenge when captain Rasad Sadiqov was sent off for bringing down Willian in the penalty area.
Hazard, starting as a false nine as Conte left Alvaro Morata on the bench, tucked home the spot-kick for his third goal in the group stage and produced a clever assist for Willian to make it 2-0 15 minutes later.
The remainder of the match was played at a procession pace, as Chelsea looked to conserve energy for Saturday's Premier League clash with Liverpool, but Fabregas added a third with 17 minutes left to play courtesy of another precise effort from 12 yards before Willian lashed home a fine fourth.
The result sends the English champions through and puts them two points clear at the top of Group C ahead of Atletico Madrid's clash with Roma, while Qarabag must hope for a favour from the Italians to preserve their hopes of snatching a Europa League spot on matchday six.
1 - Eden Hazard has both scored and assisted in a single Champions League game for the first time in his career. Schemer. pic.twitter.com/6qVnSRP0NR— OptaJoe (@OptaJoe) November 22, 2017
A lively start from Qarabag seemed to have Chelsea unsettled and they were fortunate not to be 1-0 down inside 13 minutes, with Michel rattling the crossbar from inside the penalty area after a one-two between Maksim Medvedev and Dino Ndlovu.
The home fans were in fine spirits but their mood changed completely with 19 minutes played, when Sadiqov was adjudged to have deliberately pulled Willian down by his arm as he attempted to get free in the penalty area.
The captain was duly given a straight red card and Hazard made no mistake from the penalty spot, rolling the ball into the bottom corner as goalkeeper Ibrahim Sehic went the wrong way.
It might have been a controversial way to break the deadlock but there was nothing questionable about Chelsea's second. Pedro, Willian and Hazard combined following a Cesc Fabregas ball forward, the move ending with Hazard backheeling into Willian's path, and the Brazilian made no mistake with a low finish from just inside the area.
Conte resisted the temptation to make changes at half-time but Chelsea looked keen to kill off the contest as soon as possible, with Sehic making a good save to deny Pedro one-on-one after a fine lofted pass from Fabregas.
Hazard was then denied by a fine one-handed save before he departed to a rousing reception from the travelling Chelsea fans, as Conte opted to give Morata a 25-minute run-out.
The Spain striker missed a great chance to get on the scoresheet, dragging a shot inches wide of the left-hand post from the edge of the six-yard box, and he was denied by the offside flag barely a minute later after tapping in Cesar Azpilicueta 's lay-off.
Fabregas did manage to get Chelsea a third goal, though, to cap an efficient outing from Conte's side.
Referee Jorge Sousa adjudged Medvedev to have pulled Willian's shirt into the penalty area, despite the full-back's protests that contact stopped before they crossed the 18-yard line, allowing the former Arsenal and Barcelona midfielder to sweep the ball into the bottom corner after his first effort was ruled out for encroachment.
Willian completed a superb individual display with his second goal five minutes from the end of normal time, collecting Pedro's pass before lashing beyond Sehic from 20 yards to send Chelsea through with a little bit of swagger.
Key Opta facts:
- Chelsea have booked their place in the knockout stages of the Champions League for the 14th time in their last 15 appearances in the competition.
- Qarabag have now failed to win their last six consecutive European games (including qualifiers), their longest winless streak since July 2009 (8).
- The Blues have kept four clean sheets in their last five games in all competitions, as many as in their previous 18.
- On his 200th appearance for Chelsea in all competitions, Willian scored a brace in the Champions League for the first time since November 2012 for Shakhtar Donetsk v FC Nordsjælland.
- Qarabag are only the third team to pick up a red card in three consecutive Champions League games (also Bordeaux in 2000 and Juventus in 2001).
- Eden Hazard has scored three goals in his last three Champions League appearances, as many as in his previous 19 combined.
- Hazard both scored and assisted in a Champions League game for the first time in his career.
- Cesc Fabregas became the fourth Spanish player to hit the 20-goal mark in the Champions League (also Raul 71, Fernando Morientes 33, Fernando Torres 20).