Goals from Pedro, Davide Zappacosta, Cesar Azpilicueta, substitute Tiemoue Bakayoko and a Michy Batshuayi double ensured a comfortable return to Europe’s elite after last season’s first absence since 2003-04.
Chelsea next play Atletico Madrid with the saga surrounding Diego Costa rumbling on, before home and away clashes with Roma. It is those games which will determine the Blues’ progress or otherwise.
Zappacosta’s 30th-minute strike was the highlight on Tuesday night at Stamford Bridge.
The Italian, signed on deadline day from Torino and making his Champions League debut, struck from wide on the right. It appeared to be an attempted cross which, for him and Chelsea, was wonderfully miscued.
“Zappacosta – he scores when he wants” sang the Chelsea faithful as the right wing-back moved halfway towards Costa’s Champions League tally for Chelsea.
Costa has two goals in 15 appearances in the competition for the Blues and is now almost forgotten.
Fractious relations with Costa and the Premier League opening loss to Burnley led some to suggest a crisis at Chelsea. A month on and Antonio Conte’s side have four successive wins.
Qarabag beat the champions of Georgia, Moldova and Denmark to become the first Azerbaijan side to reach the Champions League group stages.
The English champions proved a different proposition, despite Conte rotating his options for the second of seven matches in September. Arsenal are the next opponents on Sunday.
Alvaro Morata, Eden Hazard, David Luiz and Bakayoko were among the substitutes, while Batshuayi, Andreas Christensen and Zappacosta were given an opportunity.
N’Golo Kante was making his Champions League debut despite winning the Premier League in successive seasons with Leicester and then Chelsea. And the France midfielder thrived in a ruthless team performance.
Marauding left wing-back Marcos Alonso had a shot punched away unconvincingly by goalkeeper Ibrahim Sehic and then a volley blocked by Rashad Sadygov before Chelsea took a fifth-minute lead.
A short corner was worked by Willian to Pedro, who, unmarked, curled the ball in from the edge of the area.
Gary Cahill started for the first time in a month. Back following a three-match domestic suspension after his sending-off against Burnley, Cahill was over-eager in catching Pedro Henrique from behind, earning a booking.
Sehic denied Willian and Batshuayi was unable to turn in the rebound from a tight angle before Chelsea’s second.
Thibaut Courtois rolled the ball to Zappacosta, deep in his own half. He ran down the right, by two would-be tacklers and looked centrally for a target in the area.
But, with goalkeeper Sehic off his line, what appeared to be a misdirected cross found the back of the net.
Zappacosta will no doubt say it was intentional and thereafter he was encouraged to shoot at every opportunity.
Henrique had a shot held by Courtois as Qarabag refused to sit back.
Their defending was woeful and Azpilicueta stooped to head in a sublime Cesc Fabregas cross to make it 3-0 early in the second half.
Willian hit the bar before Bakayoko’s deflected effort went in after another short corner.
Next Bakayoko and Bayshuayi combined, the latter drilling in low from the edge of the area.
A Zappacosta cross was then bundled in by Batshuayi, with Maksim Medvedev hapless in his attempts to prevent the goal.
Like Zappacosta and Azpilicueta, the game marked Batshuayi’s first Champions League goals in a convincing victory.