The scoreline was not enough for the Gunners to earn a point in their first Premier League game of the season but they have a bright future ahead.
The visitors had not won in eight league games and were on the verge of going down at the break when Olivier Giroud and Theo Walcott found space in the middle of the park.
Arsenal were rewarded for their effort with three first-half goals, as Riyad Mahrez finished off the scoring with an early goal from close range.
Mahrez was given the ball and fired a shot towards the far corner, but it flew into the net off the crossbar.
Walcott also went close with a header, before Alexis Sanchez also fired a penalty past goalkeeper Hugo Lloris.
Arsenal boss Arsene Wenger said his side had the quality to keep up with the best but the home side have now got some momentum after their 4-1 defeat by Leicester on Wednesday.
“They had a good game against us but it was not the best performance we had against them.
But we have got some quality in the team and we are going to continue working on our strengths,” Wenger said.
“The most important thing is the quality we have.
It is important to have the right balance between those two things.
We are playing in the Champions League.”
Arsenal manager Arsene