Edin Dzeko scored four for City at White Hart Lane and Wayne Rooney responded with a hat trick as Arsenal allowed eight goals in the league for the first time in 115 years.
"You feel humiliated when you concede eight goals,'' Arsenal manager Arsene Wenger said. "It was a terrible day for us, it was a combination of an under-strength team and weakness.''
Arsenal has just one point after three games and has had a player sent off in each match, with defender Carl Jenkinson dismissed against the league leaders.
"The performance today was incredible and we deserved the result,'' Rooney said. "Whether or not Arsenal have a full-strength squad, every time we play them we have a go and try to score. They had some players out but that should take nothing away from us.''
Manchester United tops the standings on goal difference ahead of City as the only teams to have opened the season with three successive wins.
Tottenham, though, is stranded at the bottom after being ripped apart by big-spending City.
"Today was something special for me, to score four goals in the Premier League is fantastic,'' Dzeko said. "I think we're getting better and better.''
Also Sunday, Leon Best's second-half double clinched a 2-1 victory for Newcastle over Fulham and Ryan Shotton's late goal gave Stoke a 1-0 win over West Bromwich Albion.
At Old Trafford, United scored eight goals for the first time since 1999.
Rooney netted his first just before halftime with a perfect free kick landing in the top corner, but Theo Walcott pulled one back in stoppage time to reduce the deficit to 3-1 at the break.
There was no recovery, however. Rooney restored the three-goal cushion in the 64th by curling another free kick past Szczesny.
Nani chipped in another three minutes later before Ji Sung-Park found the bottom right corner to make it 6-1.
Even after van Persie pulled one back, Arsenal's misery continued. Jenkinson sent off with 14 minutes to go for hauling down Javier Hernandez, having already been booked.
Rooney was able to complete his hat trick in the 82nd from the penalty spot after Walcott fouled Evra, taking his United tally to 152.
Danny Welbeck and Ashley Young also scored for United.
"When you play Arsenal you expect a difficult game,'' United manager Alex Ferguson said. "We got careless at times and they made chances because they still have quality up front, but overall we are very satisfied that we kept the performance levels up.''
The performance overshadowed City's ruthless display at Tottenham earlier in the day, inspired by a lively Samir Nasri on his first appearance since moving from Arsenal.
The France midfielder provided the 34th-minute cross that Dzeko tapped home for City's first goal.
Tottenham could have quickly leveled when Bale delivered a crisp cross to Crouch, whose downward header crept wide.
City's second took American goalkeeper Brad Friedel completely by surprise, remaining static as Dzeko buried another cross from Nasri into the net with a header.
Yaya Toure supplied Dzeko's third 10 minutes into the second half, while Sergio Aguero netted after bursting into the box past Michael Dawson.
Younes Kaboul pulled one back for Tottenham, but Dzeko put the gloss on City's win in stoppage time by curling the ball into the top corner.
"This is a very long season and it's important that we started well,'' City manager Roberto Mancini said. "The next games will be very hard because now everyone thinks we will score three or four goals, but that is impossible.''
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Manchester United routs Arsenal 8-2
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