Two spot-kicks and a first half red card for Qarabag captain Rashad Sadygov helped Chelsea towards a third win from five Group C games to qualify ahead of December's home clash with Atletico Madrid.
Eden Hazard and Cesc Fabregas converted from the spot, while Willian marked his 200th Blues appearance with two sublime goals.
Chelsea have now reached the last-16 in 14 of their last 15 attempts. The exception was in 2012-13 when the Blues became the first champions to exit at the group stage.
Chelsea were the most recent English team to reach the Champions League final, in 2012, and Antonio Conte has repeatedly criticised domestic fixture schedulers for hampering chances of a repeat.
The Blues were absent from Europe in winning the domestic title in Conte's first season, but continental competition has complicated life for the Italian, whose side trail Premier League leaders Manchester City by nine points ahead of Saturday's trip to Liverpool.
Qarabag, Azerbaijan's first representatives at this stage in Europe, were beaten 6-0 by Chelsea in September, but were expected to be a far trickier proposition here after draws with Atletico in their last two games.
David Luiz, dropped for the wins over Manchester United and West Brom following the 3-0 loss at Roma, returned for Chelsea's longest European trip, but their defence appeared shaky.
Michel, the former Birmingham midfielder, fashioned an opportunity and struck a shot which rattled the crossbar after 13 minutes. Richard Almeida sliced the rebound wide.
Chelsea operated without a recognised striker, with Hazard, Willian and Pedro a mobile triumvirate up front.
Willian got in front of Sadygov and was clumsily felled by the Qarabag captain.
Portuguese referee Manuel De Sousa pointed to the spot and dismissed Sadygov for denying a clear goalscoring opportunity.
Qarabag staged an impromptu touchline teamtalk as Sadygov, who earlier in the day managed the under-19s in a 3-1 loss to their Chelsea counterparts, belatedly handed the captain's armband to Maksim Medvedev.
Hazard was made to wait to take the penalty, but he sent goalkeeper Ibrahim Sehic the wrong way for his third European goal of the season.
It was game over before half-time when Willian was on the end of a fine team move.
Fabregas' pass was flicked by Pedro to Willian. The Brazilian found Hazard, whose return pass was with his heel, and Willian made no mistake with a composed finish.
Sehic saved from Pedro and Hazard before Alvaro Morata, on for Hazard, passed wide when he should have scored.
Willian had his shirt tugged by Gara Garayev and Chelsea had a second penalty.
Fabregas converted after encroachment led to the spot-kick being retaken.
Sehic again saved from Morata but was then beaten by Willian with a fine shot from the edge of the area as Chelsea completed a comprehensive victory.