Theo Walcott scored an early brace and Arsenal appeared to be cruising when Rob Holding made it three shortly before half-time.
But BATE pulled one back through Mirko Ivanić and had a couple more chances before the half-time break.
Olivier Giroud restored Arsenal’s three goal advantage from the penalty spot but Mikhail Gordeichuk then took advantage of some slack defending to give the Belarusian side a glimmer of hope.
But the hosts were low on quality and Arsenal held on to run out comfortable winners. Here are five things we learned.
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Walcott takes his chances
With Alexandre Lacazette now firmly established as Arsenal’s first-choice striker, and with Danny Welbeck also ahead of him in the pecking order, it is vital for Theo Walcott to seize his chances in the cup competitions this season, to remind Arsene Wenger of his quality.
He did that here. Walcott opened the scoring by finishing Jack Wilshere’s exquisite cross from close-range and then doubled Arsenal’s advantage when he capitalised on BATE’s atrocious defending to fire home from just inside the box.
The 28-year-old looked sharp throughout and was a cut above the opposition whenever he found himself in possession. It was a promising night for the forward who will now be hopeful of being handed a chance in the Premier League by Wenger in the coming weeks.
Wilshere remains as enigmatic as ever
It didn’t take long for Wilshere to show off his pedigree in this Europa League fixture. Receiving an awkward pass around 30 yards from goal, he exchanged cute one-touch passes with Olivier Giroud before dinking an inch-perfect cross into the path of Walcott, who beat the hapless Denis Scherbitski at the second time of asking.
The move – not to mention his contribution to Arsenal’s attack throughout the rest of the match – was a reminder of Wishere’s quality, which has been questioned over the past few seasons. It was also a reminder of how the 25-year-old continues to frustrate: if he is capable of such outstanding performances, why can he not replicate them week in, week out?
Deployed in his favoured number 10 role, Wilshere looked on a completely different level to anybody else. But will Wenger be inclined to finally drop Mesut Ozil in favour of the enigmatic Englishman?
Tonne up for Giroud
Much-maligned French forward Giroud made it 100 goals for Arsenal in relatively understated fashion – beating Scherbitski from the spot after an incredibly soft penalty had been awarded to the away side.
It is a significant landmark for a striker who has consistently delivered in front of the goal for Arsenal, but never truly embraced by Arsenal’s fans.
Given that Arsenal spent a club-record fee on Lacazette it is highly unlikely Giroud will ever reclaim his place in the first-team but this was a performance to prove that he is more than just a fringe player.
Wenger puts his faith in youth - again
As expected, Wenger once again turned to his young guns for Arsenal's Europa League campaign. Reiss Nelson and Ainsley Maitland-Niles were both handed starts while 18-year-old Joe Willock made his senior debut for the side.
Indeed, this was Arsenal's youngest starting XI in European competition since December 2014 when the club faced Galatasaray in the Champions League. Although fans may feel aggrieved that Wenger is refusing to take the competition seriously, at least it remains a valuable way for the club's youngsters to cut their teeth on the elite stage.
BATE blow hot and cold
With Arsenal 3-0 up after 25 minutes, it was the worst possible start that BATE Borisov could have imagined. Against Wenger's visitors, the hosts looked like a League Two team in comparison. They lacked an effective press, affording Arsenal the space and time to dictate play as they saw fit. At the back, their defending was patchy at best while Scherbitski's farcical clearance for Walcott's second served as a reminder to the general gulf in quality between these two teams.
But it wasn't all doom-and-gloom for BATE. After Ivanic's goal, the home side perked up. Their football was more purposeful and threatening. Indeed, BATE could have added a second a mere three minutes after their opener.
Stasevich's delivery into the Arsenal box in the 31st minute almost found its way into the bottom left-hand corner after taking the slightest of touches. It took a fine save from Ospina to deny BATE and keep the momentum with Arsenal.
The visitors were by far the superior side but BATE certainly let their presence be felt and were eventually rewarded with a second. The chances continued to come their way, with the likes of Stasevich and Volodko both squandering opportunities in front of goal. It was a deserved win for Arsenal but by the final 20 minutes BATE had turned this into a proper game of football.