A frenetic first half somehow ended goalless despite Liverpool hitting the woodwork twice and both teams being denied by the offside flag, with Jurgen Klopp's side seeing a goal wrongly disallowed.
James Milner did finally break the deadlock for the visitors shortly after the hour mark, but Alexandre Lacazette earned Unai Emery's side a point eight minutes from time to extend Arsenal's unbeaten run to 14 matches across all competitions.
The result means that Liverpool are still unbeaten after 11 games of the Premier League campaign, moving one point clear of Manchester City ahead of the champions' home game against Southampton on Sunday.
A topsy-turvy first half began in typically high-octane fashion for a fixture which has averaged more than five goals per game over the past five league meetings, and Arsenal almost broke the deadlock after just four minutes when Lacazette's flick was well saved by Alisson Becker.
Liverpool soon began to grow into the game after Arsenal's bright start, but they were almost punished for giving the ball away when Hector Bellerin slid a pass through for Pierre-Emerick Aubameyang, whose shot was blocked by Joe Gomez.
The resulting corner was well worked for Granit Xhaka, whose first-time shot lacked the power to truly trouble Alisson, but the Liverpool goalkeeper was fortunate to get away with an error in judgement moments later.
The Brazilian came charging off his line to meet a cross, but he was beaten to the ball by an unmarked Henrikh Mkhitaryan, whose header dropped agonisingly wide of the open goal.
Just when it looked as though an Arsenal opener might be incoming, Liverpool had the ball in the back of the net. Roberto Firmino lifted his finish past Bernd Leno and saw it come back off the woodwork and fall at the feet of Sadio Mane, whose simple finish into the empty net was wrongly disallowed for offside.
The constant ebb and flow of the game soon began to swing in Liverpool's favour and they almost took the lead midway through the first half when Virgil van Dijk collected Mohamed Salah's lofted pass forward, bringing the ball down on his chest before seeing his volleyed finish thwarted by Leno.
Andrew Robertson was also denied by the Arsenal keeper shortly afterwards, while moments later Bellerin fired a first-time effort wide as the end-to-end nature of match continued.
Aubameyang then saw his shot deflect wide off Van Dijk before Firmino threw himself in the way of a Lacazette strike. The French striker had a better chance six minutes before half time when he was released by a clever flick from Mesut Ozil, only to flash his low effort wide of the far post.
Aubameyang threatened again moments later and then did finally have the ball in the back of the net, although this time the offside flag was correctly raised against Shkodran Mustafi in the buildup.
It was Liverpool who ended the half on top, though, and they almost took the lead with the final meaningful action before half time when Van Dijk got to the ball before Leno, who had rashly charged off his line but was fortunate to see the header dribble against the post.
Somehow an absorbing first half ended goalless, and the chances dried up in the opening exchanges of the second half before Liverpool did break the deadlock just past the hour mark.
It was an avoidable goal for the Gunners too, with Leno needlessly palming Mane's cross into the path of Milner, who fired home the loose ball for his 50th Premier League goal.
Arsenal almost responded immediately as Lucas Torreira carried the ball forward before letting fly, but his shot was too close to Alisson, who tipped it over the crossbar.
Liverpool went pushing for a second goal which could have taken the game away from the hosts, and they almost got it when first Mane was just short of connecting with Salah's square pass and then Firmino nodded narrowly wide from a corner moments later.
Another corner provided the visitors with a golden opportunity to double their advantage as Van Dijk was left completely unmarked, but his firm header was tipped over by Leno.
It proved to be an important save as Arsenal levelled things up eight minutes from time when Lacazette beat Alisson to Alex Iwobi's through-ball before creating space to shoot and firing a fine finish past the keeper, who was still out of position.
Just as Arsenal did when they fell behind, Liverpool threatened an immediate response with Mane and Salah both missing the target from the edge of the area, and there was also a late chance for Arsenal when Bellerin failed to make the most of Ozil's pass.
In the end the spoils were shared, though, as Liverpool dropped points for only the third time this season - although the result is still enough to lift them above Man City until at least Sunday while Arsenal remain fourth.
ARSENAL (4-2-3-1): Leno; Bellerin, Mustafi, Holding, Kolasinac (Welbeck 81'); Torreira, Xhaka; Mkhitaryan (Iwobi 68'), Ozil, Aubameyang (Ramsey 73'); Lacazette
LIVERPOOL (4-3-3): Alisson; Alexander-Arnold, Gomez, Van Dijk, Robertson; Wijnaldum, Fabinho, Milner; Salah (Matip 94'), Firmino (Shaqiri 80'), Mane