New summer signings Lukas Podolski and Santi Cazorla both found the back of the net to give the north Londoners the three points on Merseyside.
Arsene Wenger was happy with his team’s showing and also admitted that seeing the new players score was a source of pleasure.
“It’s always a test when you arrive at a club like Arsenal,” Wenger told Sky Sports.
“People have seen many, many, many great players so you have to convince people. They know what makes a good player.
“I think slowly they can convince our fans they are good enough to play for us.
“It’s like scoring goals, as long as you don’t concede everybody defends a bit better as they want to keep the record, and that helps.
“But overall credit to the whole team, they defended well,” he concluded.
Arsenal take on Southampton next at the Emirates Stadium after the international break.
By Gareth McKnight