Arsenal moved to the top of the Premier League after a first-half Kai Havertz goal was enough to take all three points off Liverpool at Anfield.
The visitors went into an early lead when Declan Rice drove into the area and cut the ball back for Havertz to tap in at the back post.
Liverpool may feel they deserved a spot-kick before the break after Jurriën Timber held the back of Alexander Isak's shirt inside the area, but the incident was cleared without further intervention.
The second period was a cagey one as Andoni Iraola's men struggled to create chances against the best defence in the top flight.
Rio Ngumoha fired wide at the start of stoppage time but Arsenal saw it out without much further issue to leapfrog Manchester City at the summit.
Gunners finally breach Anfield
Prior to Sunday's fixture, Arsenal had not won a top-flight match at Anfield since September 2012, when Lukas Podolski and Santi Cazorla got on the scoresheet -- with Mikel Arteta in midfield.
The Gunners had lost three and drawn three on Merseyside in the league under Arteta's stewardship coming into this one, including a 1-0 loss in their title-winning season, but this time were able to go that one step further.
David Raya had nothing to do until he grabbed a weak Víctor Muñoz header in the 89th minute, protected valiantly by his defensive pairing of Gabriel and Ezri Konsa.
Even without William Saliba, the Gunners effectively nullified one of the most expensive attacks in the world, as Declan Rice was once again outstanding in the middle of the park.
If they can defend like that against the top teams for the rest of the season, they will fancy their chances of defending their title.
Liverpool's 'fab four' fall short
After going behind, the hosts responded positively and began to build into the game, looking the more likely to the get the next goal.
But the equaliser did not materialise, despite some bright moments for Bradley Barcola, Florian Wirtz and Cody Gakpo who supported Isak.
Indeed, by full-time, the hosts failed to register a single shot on target, with their front four completely starved for space.
Despite that, their expected goals (xG) was higher than that of Arsenal at the end, with Barcola and Isak left frustrated by block after block inside the area.
Wirtz was unable to exert influence in the final third as clear sights of Raya 's goal came at a premium. While they opened up Brighton &Hove Albion at will in the opening spell last time out, the same dynamism and spark was lacking for Iraola's side against the reigning champions.
Should Alexander Isak have got a penalty?
With 21 minutes on the clock, Barcola whipped in a cross from the left towards the far post which went behind for a goal kick, but not without controversy.
Isak darted towards goal, looking to get onto the end of it, but was held back by Timber.
The Swede did not go down to the ground or indeed protest, instead smiling when saying something to the Arsenal full-back afterwards.
Andy Madley was not advised by VAR to look at the potential foul further -- one that may have been given if Isak hit the deck.
"The Alex [Isak] one is a clear penalty," Iraola said to Sky Sports after the match. "You hold the t-shirt, we can all see that he holds the t-shirt, the ball just goes one or two metres in front of Alex.
"Alex is going to head the ball in front of goal. If he doesn't go the floor, you're not going to get the penalty."
Asked if Isak should have "made more" of it, the Spaniard added: "That's the problem we have, with the game. Because he doesn't dive ... If he goes to the floor, they give the penalty, 100%."
Team line-ups
Liverpool: Alisson, Araújo (82'), Jacquet, van Dijk, Kerkez (82'), Nyoni (58'), Mac Allister, Barcola, Wirtz (82'), Gakpo (67'), Isak.
Subs unused: Mamardashvili, Gomez, Endō, Gravenberch.
Arsenal: Raya, Timber, Konsa, Gabriel, Calafiori, Rice, Guimarães (62'), Madueke, Ødegaard (89'), Tzolis (84'), Havertz (84').
Subs unused: Arrizabalaga, Mosquera, White, Eze, Zubimendi.
Goals: Havertz 12'