Van Dijk scored the first of Liverpool's two equalisers when he headed home from a corner kick in the 18th minute.
Bukayo Saka had earlier opened the scoring in the ninth minute. Mikel Merino and Mohamed Salah also found the net later in the match. But all of those goals came after Van Dijk was penalised for an off-the-ball foul on Kai Havertz.
In the sixth minute, with the game still tied at 0-0, Van Dijk collected the ball from Liverpool goalkeeper Caoimhin Kelleher before passing it left to Andy Robertson.
Van Dijk had been closed down by Havertz, although the German did not go as far as attempting a tackle. After the ball had gone, Van Dijk pushed Havertz away using his right hand. The former Southampton defender then appeared to aggressively and deliberately thrust his left leg into the Arsenal forward.
But Van Dijk was not issued with a card, despite many fans thinking he should have seen red
Referee Anthony Taylor awarded a free-kick but did not issue Van Dijk with a card.
Reacting to Van Dijk's foul, Sky Sports pundit Gary Neville said: 'He was stupid, Van Dijk. He's just got involved in a little tussle and sort of backed in to him.'
While watching a replay, Neville added: 'A little elbow and then that. Oh yeah, he kicks out at him as well. Silly. He doesn't really need to do it.
Multiple Gunners fans were furious with Taylor's supposed leniency.
Writing on X (formerly Twitter), one fumed: 'How the F*** has Van Dijk got away with that???? Not even a yellow card for hitting and kicking out at someone off the ball????'
Another tweeted: 'If an Arsenal player does what Van Dijk just did to Kai Havertz, VAR would have called the referee and a straight red card would have been issued.'
A similar message from a different Gunners supporter moaned: 'And this was a red card offense from Van Dijk but he wasn't wearing an Arsenal kit'.
The level of Arsenal anger only increased after Van Dijk got on the scoresheet.
'So Van Dijk equalises not long after he should have been sent off,' grumbled one fan.
Another added: 'Ah. Van Dijk who should've been sent off scores. Of course.'
Fourteen players have been sent off in the Premier League so far this season, including three Arsenal stars - Declan Rice, Leandro Trossard and William Saliba.
Sunday's result left Liverpool second in the table, one point below leaders Manchester City.
Arsenal are third, sitting four points behind Liverpool.