Kai Havertz scored the decisive goal in the 16th minute as Mikel Arteta's side held on for an important away victory, ending Liverpool's five-match winning run in all competitions.
Arsenal made a bright start and were rewarded when Declan Rice produced an excellent low cross into the Liverpool box following a loose pass from the hosts. Havertz was left unmarked at the far post and calmly finished to give the visitors the lead.
Liverpool responded strongly and created several opportunities before the break, but their finishing let them down.
Florian Wirtz came closest when his free-kick from a tight angle beat David Raya but struck the crossbar. Alexis Mac Allister then missed a golden opportunity shortly before halftime, heading over from inside the box despite being left unmarked.
Liverpool continued to dominate possession after the restart as they searched for an equaliser, but Arsenal's defence remained organised and repeatedly frustrated the hosts.
The Reds' lack of cutting edge was particularly costly, with Liverpool failing to register a shot on target throughout the match despite creating pressure in the final third.
Arsenal came close to extending their lead in the second half when Christos Tzolis fired a low effort towards the bottom corner, forcing Alisson into an excellent save.
Liverpool continued pushing in the closing stages, with Rio Ngumoha and other attacking players attempting to find a way through, but Arsenal held firm to secure a valuable three points.
The victory also ended Arsenal's long wait for a Premier League win at Anfield, with the Gunners recording their first league victory at the stadium since September 2012.
It was also Arsenal's 300th Premier League away victory, putting them alongside Manchester United as the only teams to reach the milestone.
For Liverpool, the defeat ended a run of five consecutive victories and highlighted their struggles in front of goal despite enjoying long spells of pressure.
Arsenal now turn their attention to Champions League action on Wednesday when they travel to face Slavia Praha, while Liverpool will visit Fenerbahce.
The result gives Arteta's side an important advantage at the top of the Premier League as the title race continues to take shape.
