Sokratis Papastathopoulos, Emile Smith Rowe and Matteo Guendouzi all netted their first-ever goals for the Gunners as the Premier League outfit eased to the three points in Azerbaijan on Thursday evening.
Arsenal - who have recorded eight wins in a row in all competitions - now sit on six points in Group E, with Sporting Lisbon level with the English club having fought back to defeat FC Vorskla in Ukraine.
However, Arsenal were ahead a minute later when Nacho Monreal's header from a corner was diverted into the bottom corner by Sokratis for his first goal in a Gunners shirt.
Smith Rowe had been given just his second start in the Arsenal first team and the young Englishman should have got himself on the scoresheet in the 18th minute, but his sliding effort at the back post after meeting a low Sead Kolasinac cross was sent into the side-netting.
Smith Rowe sent a scissor kick wide at the other end but shortly afterwards, Filip Ozobic was only prevented from finding the back of the net with a half-volley by an excellent save from Leno.
Emery made the decision to change to a back four at the break but it was Qarabag who benefitted from the change with the home side having a sustained period on the ball after the restart.
However, Arsenal soon doubled their advantage through 18-year-old Smith Rowe, who collected a pass from Alex Iwobi before sliding a shot under Vagner from 10 yards out.
Qarabag continued to get the ball into threatening positions but unlike in the first half, they were unable to get any shots away which were realistically going to trouble Leno in the North London outfit's goal.
Arsenal made sure of all three points with 11 minutes left when substitute Alexandre Lacazette teed up Guendouzi on the edge of the area, with the Frenchman proceeding to drill a low shot into the bottom corner.
Leno had to remain alert to keep out Abdellah Zoubir's long-range effort during the closing stages while at the other end, Welbeck sent a first-time effort well over the crossbar after neat work from Lacazette.
Both teams were still pushing for goals in three minutes of added-on time, but Arsenal held out to keep a third clean sheet in four matches in all competitions.
QARABAG (4-2-3-1): Vagner; Medvedev, Huseynov, Rzezniczak, Agolli; Michel, Qarayev (Slavchev 84'); Madatov (Delarge 61'), Ozobic (Abudullayev 67'), Zoubir; Emeghara
ARSENAL(3-4-3): Leno; Holding, Sokratis, Monreal (Torreira 46'); Lichtsteiner, Elneny, Guendouzi, Kolasinac; Smith-Rowe (Ozil 65'), Welbeck, Iwobi (Lacazette 71')