It took just four minutes for the Gunners to open the scoring against BATE after Pierre-Emerick Aubameyang's cross was turned in by defender Zakhar Volkov for an own goal.
Arsenal’s opening goal was the club's fastest in European competition since Lukas Podolski netted against Galatasaray (two minutes and one second) in the Champions League back in December 2014.
Shkodran Mustafi made it 2-0 just before half-time, heading home from Granit Xhaka's lofted corner in the 39th minute.
Substitute Sokratis Papastathopoulos then added the third on the hour mark to fully secure Arsenal's place in Friday's draw.
The Greece international's goal off the bench was the club's 13th from a substitute in all competitions this season, which is more than any other Premier League side.
The match was also Arsenal's third consecutive clean sheet at the Emirates Stadium in European competition, a feat they had not achieved since back in April 2009.
At the time, the Gunners enjoyed six straight shut-outs at home in European competition with the run eventually ending in Champions League semi-final defeat to Manchester United.
Not only does Emery have a knack of worthwhile substitutions and continental clean sheets, but he also extended his already-impressive European track record with Thursday’s win.
He took the Liga club to three back-to-back Europa League triumphs during his time there, and he now remains in the hunt to add a fourth to his collection with Arsenal this season.
Only previous Juventus manager Giovanni Trapattoni has won the second-tier European trophy as many times as Emery.