Aubameyang to the rescue for Arsenal after Leno howler
The club captain scored just four minutes after David Luiz had equalised as the Gunners fought back to win the Group B clash after a Bernd Leno mistake saw them fall behind early in the second half.
Thomas Partey made his first start for the club in a match from which Rapid will feel they should have taken something, with goalscorer Taxiarchis Fountas unable to capitalise on further Leno errors.
Rapid had 12 shots to Arsenal's 11 but could not avenge a 6-2 aggregate defeat in their only previous meeting back in the 1991-92 European Cup.
Arsenal managed more yellow cards (three) than shots on target (one) in the first half, with Thomas going into the book for a stray elbow on Fountas.
The best chances fell to David Luiz, who saw a header well saved by Richard Strebinger, and Marcel Ritzmaier, whose clever backheel almost deflected beyond Leno.
It was Leno at fault for the opening goal, though, the Gunners keeping failing to clear under pressure, allowing Fountas to drill a good finish into the bottom-right corner after the ball fell his way.
Another loose kick allowed Fountas to drive towards the penalty area, but this time Leno was on hand to block his low strike.
The Gunners drew level with 20 minutes remaining, Nicolas Pepe's deep free-kick glanced in by David Luiz, who rose unchallenged in the heart of the penalty area.
Just after another Leno error had given Fountas the chance to restore Rapid's lead, Arsenal struck again. Mohamed Elneny slid a ball through to Hector Bellerin and Aubameyang was on hand to tap in his cut-back.
What does it mean? Gunners unconvincing but up and running
This is probably the toughest of Arsenal's group games on paper, so Mikel Arteta will be thrilled to have taken all three points even if the performance left much to be desired.
He will not have been overly pleased at having to bring on Aubameyang to get the result they wanted, with Alexandre Lacazette and Eddie Nketiah ineffective.
They are level with Molde on three points, two goals scored and one conceded after the Norwegian side won away to Dundalk.
Thomas ticking along
Thomas looked comfortable at the heart of the midfield, admittedly with Rapid's central trio not offering a great deal of opposition when Arsenal had the ball.
The £45million man won five tackles, more than any team-mate, completed 90.2 per cent of his passes and contested 13 duels.
Few Arsenal players performed to their best, but Leno's loose kicking and decision-making cost his side one goal and could easily have led to two others.
Among Premier League goalkeepers since the start of 2018-19, only Jordan Pickford (11) and David de Gea (nine) have made more errors leading to goals in all competitions than Arsenal's number one.
Arsenal host Dundalk on matchday two next Thursday, after a Premier League clash with Leicester City this Sunday. Rapid's second group game is away to Molde.