The Poland international was fortunate to still be on the field after being booked for catching Laurent Koscielny with a stray elbow, but his composed volleyed finish has thrown Group F wide open - with three teams now sat on six points.
Last season's beaten finalists made the brighter start at Emirates Stadium and edged in front on 16 minutes when Aaron Ramsey wanted too many touches on the edge of his own box and Henrikh Mkhitaryan was teed up to drill low into the bottom corner.
Arsenal grew into the game after falling behind and levelled matters four minutes before the interval when Neven Subotic diverted a Bacary Sagna cross past his own goalkeeper and into the path of Olivier Giroud to crash into an empty net.
Santi Cazorla, whose introduction helped to breathe new life into the Gunners around the hour mark, clipped the crossbar with a well-struck effort, but it was Lewandowski who was to have the final say in rain-soaked north London.
Dortmund had looked lively from kick-off, with Marco Reus supporting Lewandowski as manager Jurgen Klopp watched on from the stands as he serves a UEFA touchline ban.
It was no real surprise when the Germans took the lead on 16 minutes.
Ramsey was hustled out of possession by Reus on the edge of his own penalty area, with the ball fed to Lewandowski.
The Pole played in Mkhitaryan, who smashed a low shot past Wojciech Szczesny from 18 yards.
Arsenal, who moved clear at the top of the Premier League with a 4-1 win over Norwich on Saturday, are used to having things very much their own way this season and faced perhaps their first real test of character.
Giroud showed great strength to out-muscle full-back Marcel Schmelzer and win the ball on the nearside touchline, before cutting back towards the Dortmund box where he was unceremoniously upended by Mats Hummels.
The assistant referee behind the goal was well positioned to correctly signal a free-kick just outside the box, which Koscielny headed over from Mesut Ozil's delivery.
Arsenal continued to be patient, often allowing Dortmund long spells of possession, but were level four minutes before the break.
Ramsey brought the ball forwards and fed Sagna on the overlap. His cross in behind the defence caught out Subotic and goalkeeper Roman Weidenfeller, with the mix-up allowing Giroud to smash the loose ball into the net.
The match remained delicately balanced at the start of the second period as both sides held good periods of possession, but lacked a decisive ball in the final third.
Lewandowski was somewhat fortunate to only be shown a yellow card by Sweden referee Jonas Eiksson on 64 minutes when he clashed with Koscielny.
Arsenal then came within inches of taking the lead when Cazorla's curled effort from 20 yards struck the angle of post and crossbar with the keeper beaten.
Dortmund, though, hit Arsenal on the counter attack with eight minutes left.
The ball was played out to right-back Kevin Grosskreutz on the overlap and his deep cross drifted over towards the far post, where Lewandowski arrived on cue to sweep past countryman Szczesny.