Santi Cazorla and Aaron Ramsey were the scorers on a day when Liverpool would have gone top had they won.
Brendan Rodgers’s visitors now find themselves back in third place, having briefly been in second on goal difference earlier in the day after Chelsea lost at Newcastle United.
That made it the most important domestic fixture for both sides so far this season, with Arsenal now facing Borussia Dortmund in the Champions League on Wednesday before travelling to Manchester United next Sunday.
The game was also given extra spice by Arsenal’s pursuit of Luis Suarez over the summer, when the Gunners lodged a bid of £40,000,001 ($63.7 million, 47.2 million euros) in the mistaken belief that it would trigger a release clause in the Liverpool striker’s contract.
Liverpool held on doggedly to a player who was serving a 10-match ban for biting Chelsea’s Branislav Ivanovic in April and he went into this game having scored six goals in five matches.
The game began at a frantic pace and Tomas Rosicky forced Liverpool goalkeeper Simon Mignolet into an early save.
There was quickly a chance at the other end for Jordan Henderson, who robbed Cazorla and was allowed to reach the penalty area before scuffing a weak effort at goalkeeper Wojciech Szczesny.
Arsenal’s reply was to take the lead in the 19th minute through Cazorla. The Spain midfielder was first to Bacary Sagna’s cross from the right and headed against the post before netting the rebound.
Liverpool were aggrieved when Henderson put the ball in the net after Suarez had played a free-kick to Daniel Sturridge, only for referee Martin Atkinson to rule that it had been taken too quickly.
A yellow card for Sagna for the initial foul did not appease the visitors and although Szczesny denied Kolo Toure from the retaken free-kick, the flag was up anyway.
Liverpool’s 3-5-2 formation had left them exposed down the flanks at times, but Jon Flanagan — making his first Premier League appearance since April 2012 — had been more impressive on the right than Aly Cissokho on the other side.
Rodgers changed that at half-time, with Philippe Coutinho replacing Cissokho.
It pepped Liverpool up, and Suarez in particular, as he managed to get in behind the Arsenal defence three times in quick succession, but to no avail.
Olivier Giroud should have made it 2-0 after intercepting Toure’s poor pass to Martin Skrtel, but the France striker chipped into the side-netting with only Mignolet to beat.
Arsenal did not let up, however, and were rewarded with a goal from Ramsey in the 59th minute, with the Wales midfielder finding the net from 20 yards with a swerving effort after demonstrating superior technique to set himself up from Mesut Ozil’s pass.
Suarez almost pulled one back, but saw his effort graze the far post.
Another chance came Suarez’s way late on as Arsenal switched off, but the Uruguay forward fired across goal and wide, and the hosts saw out the final few minutes with no further alarm.