A point proved enough to send Arsene Wenger's side through as BATE Borisov were beaten 5-2 away to Cologne, who remain bottom of Group H but still have a chance of advancing after their victory.
There were 11 changes to the Gunners side that beat Swansea City 2-1 in the Premier League last weekend, goalkeeper Matt Macey making his European debut in an inexperienced line-up.
Macey did his part to secure the point, tipping a header from Vujadin Savic against the crossbar as Red Star threatened to take a surprise lead into half-time.
With impressive form in this competition not enough to earn Jack Wilshere an England call-up, his frustrations were deepened when Damien Le Tallec's goal-line clearance denied him a first club goal since May 2015.
Wilshere, Theo Walcott and Olivier Giroud combined in spectacular fashion to settle the teams' meeting a fortnight prior, but could not put their experience to use and find the breakthrough here, although Wenger's side can secure top spot by winning at Cologne on November 23.
France international Giroud appeared to strain his hamstring after leaping to challenge Mitchell Donald in the air, but it did not stop him getting into a great position in the 10th minute.
Ainsley Maitland-Niles surged towards the byline on the left side of the box before squaring for Giroud, whose first-time effort was blocked by Milan Borjan at the near post.
Arsenal controlled possession but found further chances hard to come by until Giroud was slipped in by Joe Willock, who did well to dispossess Donald, but was unable to lift his shot over the onrushing Borjan.
Wenger's side could have gone into half-time behind, though, had Macey not tipped a header from Savic against the bar after the Red Star centre-back followed up Nemanja Radonjic's blocked shot.
Richmond Boakye contrived to waste another chance before the break, failing to hit the target after racing in behind Rob Holding on a swift counter-attack.
Red Star sat back after the restart and Arsenal had two claims for a penalty go unawarded, the first after slight contact between Savic and Wilshere and the second when the defender inadvertently handled the ball.
Arsenal continued to apply the pressure and a great combination between Maitland-Niles and Wilshere down the left ended with the latter seeing his goal-bound poke cleared in last-ditch fashion by Le Tallec.
Wenger sent Eddie Nketiah on for Willock in the 68th minute, but their two-goal EFL Cup hero failed to have the same impact as he did against Norwich City.
Boakye had an opportunity to snatch all three points with nine minutes remaining but he sliced wide of the near post, though the Serbian side celebrated keenly at the full-time whistle, having secured a point that moves them a point clear in second place.