The decisive moment came in the 83rd minute when Hungarian midfielder Dominik Szoboszlai converted a superb free-kick from distance, lifting the champions to victory after a demanding encounter.
Arsenal began brightly, dominating possession from the opening whistle despite an early setback.
Defender William Saliba was forced off through injury just five minutes into the match, replaced by Christian Mosquera.
Noni Madueke threatened twice during the first half, forcing Liverpool goalkeeper Alisson into saves as Mikel Arteta’s side pressed high and unsettled the champions.
Liverpool gradually grew into the game under new manager Arne Slot.
Florian Wirtz had a chance on the hour mark, and Hugo Ekitike briefly thought he had scored before being ruled offside.
Arsenal’s intensity faltered in the final quarter, with Martin Zubimendi conceding a foul on the edge of the box.
Szoboszlai stepped up and delivered a stunning strike past goalkeeper David Raya to seal the win.
The result ensures Liverpool remain the only Premier League team with a perfect record this season, demonstrating what Slot called the “character of champions.” The Reds will resume domestic duties in September against Burnley before hosting Atlético Madrid in the Champions League.
For Arsenal, the defeat was a setback after a strong performance in large parts of the game.
New signing Eberechi Eze made his debut but could not shift the outcome.
With six points from three games, Arsenal head into the break in third place, behind Chelsea, and will return against Nottingham Forest in the league followed by a European fixture against Athletic Bilbao.
Szoboszlai, who contributed in both defence and attack, was widely praised as the standout performer.
Arsenal forward Viktor Gyökeres struggled to impose himself against Liverpool’s physical back line, marking a frustrating evening for the visitors.
Despite the narrow margin, the match reflected the fierce competition expected this season between Liverpool, Arsenal, and other top challengers for the title.