In front of a sparse crowd, surprise starter Lacazette fired home 16 minutes into the match to earn the Gunners their fifth win in six Group E outings.
With top spot and a place in the last 32 already secured before kickoff, an experimental Arsenal side struggled to get out of first gear against the Azerbaijani champions on a largely forgettable evening.
Unai Emery made nine changes on the back of the 1-0 win over Huddersfield Town here four days ago that kept his side's momentum going, bringing in Laurent Koscielny for his first appearance in seven months and Mesut Ozil for his first outing in a month.
It was one of those retained from the Huddersfield game that opened the scoring for the Gunners, with Lacazette powering the ball across Vagner into the far corner of the net once slipped in by Ozil.
Lacazette's moment of quality aside, though, the first half offered little in the way of entertainment as both sides showed little urgency.
Debutant Bukayo Saka cut inside and curled a deflected shot on target, which Vagner did well to push aside, but that would prove to be it in terms of notable first-half action.
Emery had a number of youngsters on the bench for this concluding Group E match, watched by a third-full Emirates Stadium, but he held off from using any of them until 25 minutes from the end when Zech Medley was brought on for his home debut.
Medley's arrival meant Ainsley Maitland-Niles pushing into a more advanced position, and the versatile wideman set up Saka for a good chance 20 minutes from time - the youngster seeing his shot deflect narrowly wide, before his next attempt from further back was gathered by Vagner.
Emery replaced Koscielny - the only starter to boast a 100% pass-completion rate - for the final quarter of the match as Arsenal continued to go through the motions.
Eddie Nketiah, who played a big part in what turned out to be the winning goal with his tackle high up the pitch to turn over possession, had a swooping header correctly ruled out for offside in the final 15 minutes.
There was also a late chance for Saka to become Arsenal's youngest scorer in Europe at just 17 years old, but he blasted his close-range shot right in Vagner's face.
ARSENAL (4-2-3-1): Martinez; Jenkinson, Sokratis, Koscielny (Monreal 72'), Maitland-Niles; Elneny, Willock; Saka, Ozil (Gilmour 83'), Nketiah; Lacazette (Medley 63')
QARABAG (3-5-2): Vagner; Rzezniczak (Ozobic 85'), Sadiqov, Huseynov; Medvedev, Slavchev, Qarayev, Michel (Abdullayev 61'), Guerrier; Madatov (Quintana 75'), Zoubir