Unai Emery's side were caught cold in sub-zero temperatures on the stroke of half-time, Stanislav Dragun's header ending their run of five successive clean sheets in the competition.
Alexandre Lacazette had a potential equaliser ruled out for offside before he was shown a straight red card for throwing an elbow at Aleksandar Filipovic in the closing minutes.
Even when they had 11 men, the Premier League side struggled to capitalise on their territorial dominance, leaving them with a deficit to overturn in the return fixture next Thursday.
3 - Arsenal have lost three of their last four away games in all competitions (W1), as many as they had in their first 14 combined under Unai Emery (W8 D3 L3). Stutter. pic.twitter.com/iUEUrbnttv— OptaJoe (@OptaJoe) February 14, 2019
Considering the freezing conditions, Arsenal unsurprisingly took their time to warm to the task at hand.
The visitors' only chance of note in the opening half saw an unmarked Lacazette carelessly head over the top after being picked out by Sead Kolasinac's inviting cross to the back post.
Dragun did not make the same mistake at the opposite end when getting on the end of a free-kick from captain Igor Stasevich, though, giving BATE the lead with an impressive header that curved over Petr Cech.
The Gunners had been spared from conceding earlier in the game by the woodwork, Nemanja Milic flicking the ball against a post from point-blank range when trying to provide the finishing touch to Maksim Skavysh's dangerous low delivery.
Lacazette did locate the net from another Kolasinac delivery from Arsenal's left soon after the break, only for the referee's assistant to correctly raise his flag against the over-eager Frenchman.
The former Lyon star also found the target when flinging his arm back into the face of Filipovic when under pressure from the defender, forcing his side to finish a frustrating evening a man down.
What does it mean? Gunners draw a blank
Distant onlookers in the Premier League title race – fifth-placed Arsenal sit 15 points behind Manchester City and Liverpool – and knocked out of both domestic cups, Europe offers Emery his final hope of securing a trophy in his first season in charge.
The Spaniard – a Europa League specialist after lifting the trophy for three successive seasons during his time in charge of Sevilla – will expect his squad to still progress, yet this was another low in an up-and-down campaign.
Stasevich leads from the front
Dragun grabbed the goal, but Stasevich was the architect with a glorious set-piece delivery from deep. BATE's captain also had his side's best effort in the second half, forcing Cech into a smart save during a relatively rare foray into Arsenal territory.
Lacazette sees red
Given the chance to lead the line again with top scorer Pierre-Emerick Aubameyang – who missed last weekend's win over Huddersfield Town through illness – starting the game on the bench, Lacazette summed up his side as a whole with a slack performance. His first-half miss was poor, while an eagerness to make amends saw the striker make his move too soon with the disallowed goal.
Key Opta Facts
- Arsenal have lost three of their last four away games in all competitions (W1), as many as they had in their first 14 combined under Unai Emery (W8 D3 L3).
- Arsenal are just the second English team to suffer defeat against an opponent from Belarus in European competition, after Everton in December 2009 (0-1 v BATE in the Europa League).
- Arsenal have been eliminated from each of their last six two-legged ties in European competition when losing the first leg – the last such tie they managed to reverse was against Porto in the Champions League in 2009-10 (6-2 on aggregate).
- Stanislav Dragun's headed opener for BATE was the first goal Arsenal have conceded in the Europa League since matchday one against Vorskla Poltava, ending a run of five games and 495 minutes without allowing one.
- Arsenal have now kept just two clean sheets in their last 14 games in all competitions, with their last one away from home coming at the start of January (3-0 v Blackpool in the FA Cup).
- Alexandre Lacazette's red card was the first shown to an Arsenal player in European competition since March 2017, when Laurent Koscielny was dismissed against Bayern Munich in the Champions League.
Arsenal’s FA Cup exit at the hands of Manchester United last month means the next game for both teams is the second leg at Emirates Stadium.