Kai Havertz scored the only goal of the game in the 14th minute, netting at the far post after Declan Rice delivered a ball across the six-yard box from the right.
The strike gave the champions their first win at Anfield in 14 years.
Liverpool had 28 touches in the Arsenal box before the break, the most on record (since 2008/09) by any side in the first half of a Premier League game, according to Opta.
They pressed for an equaliser for the rest of the game, but found Arsenal - who have only conceded five goals in the league so far this season - to be resolute without the ball, and the final whistle went without The Reds making any impression on David Raya's goal.
Liverpool had 17 shots without making a dent. Arsenal, by contrast, had 10 shots in total, with three of them having been on target.
The result meant that Mikel Arteta’s side took advantage of Manchester City’s home defeat to Brighton & Hove Albion on Saturday to go clear at the top of the table.
Rice reflected on the "waves and waves" of attacks his team had faced after the game.
The midfielder told Sky Sports: "That is the Anfield way, that is what this Liverpool team can do. They just create waves and waves of attack, relentless attacks.
"We knew it wouldn't have been easy, but, in the end, that defensive line and that togetherness is undefeated, [like] nothing I have ever seen before."
Asked about the league table, Rice said: "You can only take the table seriously in the February, March games. Anything between now and then, you have to just win."
"We play at home, we had some opportunities," he said. "We tried everything. We could have done a bit better in the last 15 minutes to get more balls in the box.
"It wasn't enough today, and that's why disappointment is the feeling I'm having."
Havertz, meanwhile, became the all-time leading German goalscorer in the Premier League with his goal, the strike taking his total in the division to 46, ahead of Ilkay Gundogan (45), per Opta.
Speaking to Sky Sports, Havertz said: "It [the win] means a lot to the football club. We're all happy that we gave it to them."
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Kai Havertz celebrates his goal Image credit: AFP
Havertz was quick to credit Rice for his contribution to his landmark strike in English football, saying "90% of the goal belongs to that man".
He added: "It was a brilliant overlap, and a perfect cross for me. It was an easy tap-in."
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