The Blues dominated from start to finish at Stamford Bridge, with Pedro, Davide Zappacosta, Cesar Azpilicueta, Tiemoue Bakayoko all getting on the scoresheet before a late own goal from Maksim Medvedev completed the rout.
It took just four minutes for Chelsea to create their first chance of the night with Marcos Alonso being denied from 14 yards out but moments later, Pedro gave his side the lead with a wonderful effort into the corner from the edge of the box.
Qarabag were all over the place at the back but to their credit, Gurban Gurbanov's team were doing an effective job in keeping openings down to a minimum.
Chelsea would have to wait until the 19th minute for their next couple of chances, with Willian's low effort being parried by goalkeeper Ibrahim Sehic and into the path of Batshuayi, who fired into the side-netting from an acute angle.
Just before the half-hour mark, Chelsea had their second through Zappacosta, who drilled an effort inside the near post from the right flank, although his strike appeared to be intended for a teammate in the middle.
As half time approached, the tempo dropped considerably but Qarabag showed that they should still be taken seriously at the other end as Pedro Henrique cut inside onto his left foot before forcing a solid save out of Thibaut Courtois.
After the restart, there were signs that both Chelsea and Qarabag understood that the game was effectively over as a contest and the home team put the result further beyond doubt when Azpilicueta glanced a header into the roof of the net from eight yards after meeting Cesc Fabregas's cross.
The third goal gave Antonio Conte the chance to introduce Eden Hazard in order to step up the Belgian's recovery from a fractured ankle, but the attacker remained on the periphery of the game for much of the final half-hour.
Willian went close to a fourth when rattling the crossbar from inside the penalty area, but the Blues extended their advantage through Bakayoko, who sent a deflected shot into the roof of the net after Qarabag had failed to clear a corner.
Batshuayi had shown some impressive touches in and around the penalty area, but the forward finally netted the goal his play deserved when he drilled a low strike into the bottom corner from 20 yards out.
Qarabag were tiring, but Chelsea were in no mood to take it easy on the minnows, with Batshuayi forcing Medvedev to bundle the ball into his own net after Zappacosta had given all the time that he wanted to move into a crossing position.
Dino Ndlovu squandered a late opportunity for the visitors when blazing over the crossbar from 16 yards out, but conceding a late goal would have been harsh on Chelsea who displayed their strength in depth after Conte had opted to make five changes to his starting lineup.