Sergio Aguero gave City a 14th-minute lead, with Alvaro Negredo restoring the hosts' advantage after Theo Walcott had marked his first start for Arsenal since September by equalising.
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," said City manager Manuel Pellegrini.
"We are three points behind. We must continue working and improving because we have a lot more things to improve."
Having won all eight of their home games this season -- scoring 35 goals -- City climbed to third place in the table, with Chelsea moving up to second by narrowly beating Crystal Palace 2-1.
Liverpool could reclaim second place by winning at Tottenham Hotspur on Sunday, when Manchester United are also in action at Aston Villa.
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.
Walcott struck again in the 63rd minute, collecting a dinked pass from Ramsey and shaping a shot into the top-right corner, but Silva immediately converted a low cross from Jesus Navas to restore City's two-goal lead.
Fernandinho then scored 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.
Victory momentarily took City up to second place, but they slipped to third after Chelsea's win at home to Palace, which left Jose Mourinho's side two points behind Arsenal.
Ramires struck the winning goal with a sweet 20-yard drive 10 minutes prior to half-time, after Fernando Torres's close-range opener for the hosts had been cancelled out by Marouane Chamakh's volley.
"We created a lot of chances, but did not kill off the game," said Chelsea manager Mourinho, whose side visit Arsenal a week on Monday.
"Everyone is in there, but next weekend is between the first and the second and this country is waiting for that."
Everton clambered above city rivals Liverpool and into the top four after winning 4-1 at home to Fulham.
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.
Fulham slipped below Palace to 19th, with both sides now a point behind fourth-bottom West Ham United, who were held 0-0 by bottom club Sunderland at Upton Park.
Newcastle United moved above Spurs 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.
Meanwhile, Cardiff City moved four points clear of the relegation zone after Peter Whittingham's brave second-half goal gave the Welsh side a 1-0 win at home to West Bromwich Albion.
In the day's late game, mid-table Hull City and Stoke City were left to rue missed opportunities to move further away from the relegation zone after they played out a goalless draw at the KC Stadium.