Mikel Arteta’s side delivered a disciplined performance to claim all three points, with Havertz finding the net in the 16th minute after a well-worked attacking move involving Declan Rice.
The result moved the reigning champions three points clear at the top of the Premier League table, strengthening their position in the title race.
It was also Arsenal’s first league victory at Anfield since September 2012, when Arteta was still playing for the north London club.
Havertz punishes Liverpool's defensive mistake
Arsenal made the breakthrough after capitalising on Liverpool’s attempt to build from the back.
The visitors pressed aggressively and forced an error in possession, allowing Martin Ødegaard to help initiate an attack that eventually reached Rice on the right flank.
The England international delivered a low cross into the penalty area, where Havertz arrived at the far post to guide the ball beyond Alisson Becker in the 16th minute.
Liverpool attempted to respond immediately, with Alexander Isak coming close after meeting a dangerous delivery from Bradley Barcola, but the striker could not make sufficient contact.
The hosts continued to push forward and came close to equalising when Florian Wirtz struck the crossbar with a dangerous free-kick.
Alexis Mac Allister also missed a promising opportunity, heading over from close range after meeting Milos Kerkez’s cross.
Arsenal withstand Liverpool pressure
Liverpool increased their attacking intensity after the interval, searching for an equaliser against an Arsenal side determined to protect its advantage.
Isak fired over from a tight angle, while the visitors relied on their defensive organisation to frustrate the home side.
Arsenal goalkeeper David Raya was not seriously troubled by Liverpool’s attacking efforts, as the hosts struggled to turn their possession into clear-cut opportunities.
Alisson, meanwhile, produced an important save to deny Christos Tzolis, who threatened to extend Arsenal’s lead in the second half.
Liverpool continued to search for a breakthrough, but Arsenal defended resolutely to preserve their narrow advantage until the final whistle.
Liverpool left frustrated by penalty appeal
The match also featured a major talking point involving Jurrien Timber and Isak.
Liverpool believed they should have been awarded a first-half penalty after Timber appeared to pull the Swedish striker’s shirt as he attempted to reach a cross.
However, the referee and VAR did not award a spot-kick, leaving the home side frustrated.
Liverpool finished the contest without registering a shot on target, despite attempting 17 shots during the match.
Arsenal strengthen Premier League title bid
The victory represents a major statement from Arsenal, who demonstrated their ability to grind out an important result away from home.
Ending their long wait for a league victory at Anfield will also provide a significant confidence boost as the season progresses.
For Liverpool, the defeat was another setback under manager Andoni Iraola, with the Reds left nine points behind Arsenal in the league standings.
Arsenal will now turn their attention to their next league assignment against Hull City, while Liverpool will look to respond when they face Crystal Palace.