The Gunners settled into a spell of early possession at Anfield, but they struggled to do much with it at first, and David Raya had to be off his line sharply to prevent Bradley Barcola from racing clean through on the counter-attack.
However, the champions clinically converted their first meaningful chance, when Kai Havertz arrived at the far post to tap in an inch-perfect cross from Declan Rice.
A loose touch from Ezri Konsa gave Barcola a chance to provide an instant response, but the Frenchman’s touch let him down and Rice was able to intervene.
Having weathered Liverpool’s initial response, Mikel Arteta’s side could have doubled their advantage had Jurrien Timber not inadvertently blocked Noni Madueke’s pass across goal.
But Liverpool were certainly growing into the contest, and it took an important intervention from Raya to stop Alexander Isak from poking Virgil van Dijk’s header over the line.
Arsenal creaked under the pressure, as a Florian Wirtz free-kick struck the bar and Alexis Mac Allister sent a free header over the top, but they made it to the break with their lead intact.
Surprisingly, Raya didn’t make a save in the first half, despite coming up with more than one vital contribution.
Isak had a presentable chance to put that right, having been fed by Milos Kerkez, but he fired over the top as the angle closed.
Arsenal gradually succeeded in taking some of the pace out of the contest, and at the other end, Alisson was called into action to make a superb stop, tipping Christos Tzolis’ curling effort around the post at full stretch.
Tempers flared as tensions rose, and Mac Allister earned a yellow card for an altercation with Martin Odegaard, while Madueke escaped further punishment after slightly inclining his head in the Argentine’s direction at close proximity.
That proved to be the last real action, meaning that Arsenal come away celebrating a 17th win in their last 20 league matches.
The rare Anfield triumph is also their 300th away win in the Premier League, joining Manchester United as the only other side to reach that milestone.
Flashscore Man of the Match: Declan Rice (Arsenal)
