Qarabag had Rashad Sadygov sent off for a professional foul during the early stages, and Chelsea took full advantage as Eden Hazard and Cesc Fabregas got on the scoresheet to complement a fine display from Willian, who was making his 200th appearance for the club.
Chelsea have moved to the top of Group C, but Antonio Conte must now wait on the result of the game between Atletico Madrid and Roma before finding out what his side need to do in their final match in order to progress as group winners.
The first chance of the game went to Chelsea with Fabregas drilling a low shot too close to goalkeeper Ibrahim Sehic, but Qarabag should have gone in front before the quarter-hour mark only for former Birmingham City midfielder Michel to lash the ball against the crossbar from 12 yards out.
However, the decisive moment in the match came in the 19th minute when Sadygov was sent off for a professional foul after pulling down Willian when the Brazilian was about to get a shot away in front of goal.
Hazard stepped up and made no mistake from the penalty spot, and it led to the Premier League coasting through the remaining minutes of the first half while also looking for the second goal which would realistically end the match as a contest.
Fabregas scuffed a half-volley wide of the post, while David Luiz headed off target under pressure from a defender, but the visitors eventually doubled their advantage in style.
After Hazard received the ball inside the penalty area, the Belgian international flicked the ball into the path of Willian and the playmaker made no mistake in sliding it into the bottom corner from 12 yards.
Chelsea returned for the second half aware that the game was probably already won, but it did not stop Conte from telling his side to push on for a third.
Pedro should have got his name on the scoresheet when running onto a delightful pass from Fabregas, but Sehic came out to make a smart block from the attacker.
Hazard also went close after finding space inside the penalty area, but after his well-struck shot appeared destined for the far corner, Sehic got two hands in the way to punch the ball away from goal.
Qarabag were offering nothing in the final third, and Chelsea's next goal finally arrived when Willian won a second spot kick for his side after having his shirt pulled by Gara Garayev.
Fabregas was forced to retake his penalty after encroachment from several of his teammates, but the midfielder scored at the second time of asking as he slotted the ball just inside Sehic's right-hand post.
Willian had been Chelsea's star performer on the night and he deserved his second goal after running across the edge of the penalty area before drilling a shot into the bottom corner from 20 yards out.
Substitute Alvaro Morata went in search of a fifth for Chelsea as the Spaniard targeted a goal for a third successive match, but Conte's men settled for just the four as they now turn their attention to a Premier League date at Liverpool on Saturday evening.