The win sends the north Londoners up to third in the Premier League table as they won their fourth consecutive match.
Wenger’s men are playing catch up with Pep Guardiola’s Man City – five points ahead of the Gunners – after losing on the opening day to Liverpool, but they have since gone unbeaten.
Alexis Sanchez netted on his 100th Arsenal appearance, while Theo Walcott and Mesut Ozil were also on the score sheet as the French manager celebrates 20 years in charge with an emphatic victory over their rivals.
After our live national commentary, Wenger told talkSPORT: “My job is to win football games so when I win I feel we have done it well. It was done with style, steel, commitment, pace and good team play.
“I think our team play gave them big problems and we connected quickly together and I am pleased with the first half especially.
“Today was one of these days you enjoy when you are manager, but don’t worry we have suffered enough. Today was a day from goalkeeper to centre forward, everybody played well.”
Antonio Conte’s men have now lost two consecutive league matches, following the defeat to Liverpool at Stamford Bridge, and they were poor on the day as the club lost their first league match at the Emirates since 2010.
Was the three-goal win due to the Blues’ dismal showing?
“It is always difficult to say,” said Wenger.
“I think we were that good but was it because they were that bad? I don’t think so because I can only assess my team’s performance and for that I am very happy.”
The Gunners prepared for the match without Olivier Giroud, as the French striker passed a late fitness test and was named on the bench, but with Alex Iwobi, Sanchez and Walcott up front the Arsenal attack thrived and looked dangerous on pacy breaks.
After extending their unbeaten run to five in the league and seven in all competitions, Wenger admitted a win over Chelsea was vital in their bid for a first title in 13 years.
“I said to the team we are on the way up and today was a big hurdle for us to see if it is true or not true and the way we performed today suggests we are improving, going up in performances and quality.
“That is good ingredients and the pace with which we played was impressive.”
On celebrating his remarkable two-decade milestone with a win, the 66-year-old Frenchman added: “It means more to me because it was a big game and if you want ambition in the championship you need to win big games.
“We started with a defeat at home and that is not the best possible way to prepare to go into a season and we have responded very well. After six weeks we have regressed well. Let’s show we can be consistent.”
Listen to Arsene Wenger’s interview with talkSPORT in full, above…