Mikel Arteta's side actually took the lead via a fortunate goal from Alexandre Lacazette, but the champions responded quickly with an equaliser from Sadio Mane before a second from Andy Robertson.
In the dying minutes, substitute Diogo Jota made it 3-1.
But, who were the outstanding individual performers on the night?
1. Trent Alexander-Arnold - 7.9
Liverpool enjoyed the vast majority of possession on the night, and although they controlled most of the proceedings, they had to rely on one moment of luck and one piece of excellence to turn the scoreline around after going a goal behind.
The moment of excellence came for the second goal via a vintage Trent Alexander-Arnold cross which was beautifully curled from the right wing to the back post for his fellow full-back, Robertson.
With the Gunners sitting deep, Alexander-Arnold saw plenty of the ball, enjoying 103 touches on the night. He completed 52/69 passes to team-mates, with 17 of these balls being played into dangerous areas in the final third.
Arsenal were forced to be on alert each time he had the ball as he sent eight successful crosses into the box.
Three out of four duels won plus eight interceptions, too, so he worked hard.
2. SADIO MANE - 7.6
Mane was again the best performer of Liverpool's talented front three.
However, he was slightly lucky to stay on the pitch after throwing his arm into the face of Kieran Tierney only a few minutes in. He received a yellow, but a dismissal wouldn't have been out of the question.
Mane remarkably misplaced just four out of 38 passes which is impressive considering he was constantly surrounded by Arsenal defenders, who retreated into a back five whenever the hosts had the ball.
He sent 23 passes into the final third and had 10 touches inside the Arsenal box.
3. ANDY ROBERTSON - 7.4
Liverpool's full-backs were both superb on the night, and they had to be, as with Arsenal sitting deep they had the ball on the flanks more than anyone. Like Alexander-Arnold, Andy Robertson constantly fired crosses into the box, with 12 of his balls making their way inside.
Despite being deployed as a full-back, he could regularly be found as one of Liverpool's most advanced players and this was the case for the second goal as he latched on to a cross from the right to take the touch before flashing a finish under the keeper.
He enjoyed the fourth-most touches of anyone in this round of Premier League fixtures with 125.
Unfortunately for him, he did make a mistake with a sliced clearance which led to Arsenal's opener.
GAME TO FORGET
Pierre-Emerick Aubameyang had one of his least effective games for Arsenal in a while, as he was desperately isolated on the left wing. He spent most of his evening following Alexander-Arnold on the overlap, which he didn't do too well.
Incredibly, he completed just eight passes on the night.
Zero goals, zero assists, zero shots on target, zero shots.
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