The result left Arsenal first in the Premier League on 37 points, five ahead of Manchester City who lost at home to Brentford earlier in the day.
The Norwegian striker scored a brace in a 3-1 win for Pep Guardiola's side.
Robert Lewandowski picked up the best striker award named after Gerd Muller.
The champions lost their unbeaten start to the Premier League season in a heated thriller that saw home coach Juergen Klopp red-carded.
City drubbed Southampton 4-0 with Erling Haaland scoring again.
Pep Guardiola's City crushed United 6-3 in the Premier League on Sunday.
Jack Grealish and Phil Foden also scored in the 3-0 win for Pep Guardiola's side.
Haaland grabbed an outrageous 84th-minute winner against his former club.
Erling Haaland scored again but Gerrard's Aston Villa secured a 1-1 draw against Manchester City.
Newcastle United's record signing Alexander Isak scored on his debut to put his side ahead at Anfield but Liverpool snatched a 2-1 victory deep in stoppage time through Fabio Carvalho.