The visitors came from behind to finish 4-3.
Philippe Coutinho scored twice for Liverpool while Adam Lallana and Sadio Mane were also on target.
Theo Walcott Alex Oxlade-Chamberlain and Calum Chambers scored the Arsenal goals.
Manchester United got off to a winning start in the Premier League under Jose Mourinho.
They eased to a 3-1 victory at Bournemouth in their opener.
Summer signing Zlatan Ibrahimovic added to goals from Wayne Rooney and Juan Mata.
