City lost Aguero to injury early in the second half but a brace from Fernandinho, a David Silva strike and a Yaya Toure penalty secured victory for the 2012 champions, with Walcott and Per Mertesacker replying in vain.
"It's not easy to score six goals against Arsenal, the best defence in the Premier League, the best team this year," City manager Manuel Pellegrini said.
"We are three points behind. We must continue working and improving because we have a lot more things to improve."
Arsenal, meanwhile, have now lost three times this season, and manager Wenger said: "Overall, they deserved the win. We have to go home and recover and come back for the next time. We made too many technical mistakes today."
Held 1-1 at Southampton last weekend, City made a determined start at the Etihad Stadium and took the lead in the 14th minute.
Samir Nasri's right-wing corner was headed on by Martin Demichelis and Aguero hooked home a waist-high volley at the back post to notch his 15th goal in 13 games.
Walcott levelled in the 31st minute, bobbling a shot home from a Mesut Ozil pass after Aaron Ramsey robbed Toure, but Negredo restored the hosts' advantage when he tucked in a low cross from Pablo Zabaleta.
To make matters worse for Arsenal, centre-back Laurent Koscielny had to be stretchered off after cutting his knee as he slid in alongside Negredo, with the club announcing via Twitter that he had suffered a "deep laceration".
City saw Aguero limp off early in the second half but they extended their lead in the 50th minute when Fernandinho picked up a loose pass from Ozil and curled a sublime finish around Wojciech Szczesny.
Olivier Giroud squandered two chances to reduce the arrears, volleying over from a Jack Wilshere pass and then heading Bacary Sagna's cross fractionally wide, before Walcott struck again in the 63rd minute.
Ramsey dinked a pass behind the City defence for the England forward, who collected the ball and shaped a graceful shot into the top-right corner.
However, Silva converted a low cross from Jesus Navas shortly after and Fernandinho then dinked home his second goal before Mertesacker headed in an injury-time consolation for Arsenal, only for Toure to complete the scoring from the spot after Szczesny tripped James Milner.
Ramires struck the winning goal with a sweet 20-yard drive ten minutes prior to half-time, after Fernando Torres's close-range opener for the hosts had been cancelled out by Marouane Chamakh's volley.
Dimitar Berbatov equalised for Fulham with a 67th-minute penalty after Leon Osman had curled Everton ahead in the first half, but Seamus Coleman, Gareth Barry and Kevin Mirallas scored late goals to secure the points for Roberto Martinez's side.
Newcastle United moved above Tottenham Hotspur on goals scored after drawing 1-1 at home to Southampton, for whom Jay Rodriguez netted a 65th-minute equaliser after Yoan Gouffran had put the hosts in front.