There was no manic celebration from Antonio Conte and his players at the final whistle, polite handshakes replacing joyful punches of the air, but all in the visitors’ ranks could take pride in a job professionally done. Comfortable victory in Baku has extended Chelsea’s Champions League campaign into the new-year knockout phase. They may not appreciate it at Anfield on Saturday, when aching limbs will kick in as they heave to deal with a wounded Liverpool, but the 5,000-mile round trip to Azerbaijan has been distinctly worthwhile.

The final group game against Atlético Madrid, a daunting prospect when the section was drawn, will now merely determine the leadership of the section. “We have reached our first target: to go through into the knockout,” Conte said. “And to avoid the game with Atlético becoming decisive for us is very important. It will be a good chance now to have another rotation with my players.”

In a crammed schedule in which margin for error has always felt so slim, testing the head coach’s mood as much as his players’ fitness levels, a relatively relaxed evening in early December is to be cherished.

Qarabag 0-4 Chelsea: Champions League – as it happened Read more

In the context of what ultimately felt a comfortable night’s work it was easy to forget that Qarabag, much improved from the side who sunk without trace at Stamford Bridge on debut at this level in September, had initially threatened their visitors. Indeed, had their former Birmingham City midfielder Michel converted an early chance rather than clip his shot against the crossbar when it had seemed easier to score early on, then this could have been a distinctly more awkward occasion. Instead the hosts were blunted by Rashad Sadygov’s dismissal and Chelsea’s busy energy duly prevailed.

Conte could admire the grace with which his players manoeuvred the ball, with David Luiz successfully reintegrated after his spell out of favour and the side efficient and untroubled once ahead.

The head coach has now seen his team win successive away games 4-0 and was even able to withdraw the excellent Eden Hazard and overworked Marcos Alonso – his only fit left wing-back – long before the end, with the only disappointment his reluctance to blood the 18-year-old Dujon Sterling from the bench. Given the formality the contest had become, capped by Willian’s blistering fourth goal rasped in from distance near the end, a European debut might have added to the general sense of satisfaction. Sterling will have to wait.

Many of the locals had departed by the time Willian plundered his second five minutes from time, exploiting space just outside the penalty area to beat the diving Ibrahim Sehic. The majority left choked in anticlimax, those encouraging draws against Atlético buried beneath another avalanche of Chelsea goals, and grumbling at the perceived eccentricities of the referee, Manuel de Sousa. The Portuguese had spied Sadygov’s clumsy touch on Willian’s back 19 minutes in, the Brazilian crumpling to the turf to claim the penalty with the captain, much to his own bewilderment, duly dismissed.

Gurban Gurbanov, the home team’s manager, reluctantly conceded the offence may have warranted a penalty, but the double punishment seemed harsh and leant itself to conspiracy theories. “Maybe if we were not a small country and a small team, the decision might have been different,” he offered. “Chelsea didn’t need that red card.” The crowd wailed their disapproval when the incident was replayed on the big screens at half-time, and had further cause to vent their spleen at De Sousa before the end.

Regardless, this became a procession from the moment Hazard converted from the spot, becoming Belgium’s leading scorer – with eight – in the Champions League. Conte will have purred at the ease at which his players carved open opponents now steeled merely to defend, particularly for their second: a culmination of crisp and accurate passes between Cesc Fàbregas, Pedro, Willian and Hazard. The Belgian eventually back-heeled his assist square, dizzied markers failing to anticipate such impudence, for Willian to collect and calmly finish beyond the helpless Sehic.

The goalkeeper excelled thereafter to deny Pedro, Willian and Hazard – a live-wire front three, buzzing disconcertingly around panicked defenders – and should not have been given a chance by the substitute Álvaro Morata, who steered a shot wide from close range without a marker in sight. Instead Gara Garayev’s tug on Willian’s shoulder, yanking back his shirt, was penalised by the referee for another soft penalty award. “A little bit of contact,” the Brazilian said post-match. “So, for me, it was a penalty. I don’t think you guys thought it was …” The locals definitely did not, but Fàbregas converted at the second attempt anyway.

They ended up with 10 goals to show from two brushes with Qarabag – a tally that damns Diego Simeone’s Atlético all the more – and reason to believe the recovery is complete from the shambles in Rome. There was praise for the team’s “character”, “commitment” and “great desire to fight”, which is just as well because there would hardly have been time to cram in another group dressing down, like that endured at Cobham after the humiliation in Italy, before the game at Anfield on Saturday. Instead, key players have demonstrated some zest and others have been rested with Liverpool in mind. They may be patched up, their preparations rushed, but Chelsea will travel to Merseyside buoyed by European progress.