Manuel Pellegrini got the better of David Moyes in their first battle as managers of the Manchester clubs with the 4-1 win made possible by a brace from Sergio Aguero.
The Argentine opened the scoring in the 16th minute when he cleverly volleyed home Aleksandar Kolarov's cross from the left before Yaya Toure added a second on the stroke of half-time when he turned in Alvaro Negredo's knockdown header from Samir Nasri's corner.
City went three ahead early in the second half when Negredo found Aguero on the edge of the six-yard box for the former Atletico Madrid man to slot home with a side-footed volley before Nasri powered home a volley of his own from Jesus Navas' back post cross in the 50th minute.
United managed to pull one back three minutes from time courtesy of a sublime free-kick from Wayne Rooney but the damage had been done as City went third on the Premier League table with the reigning champions dropping to seventh.
Club-record signing Mesut Ozil was the catalyst for the Gunners, having a hand in all goals, as Arsene Wenger's men scored their trio of goals from set pieces.
The opener came in the fifth minute when Aaron Ramsey was on hand to slot home from close range after Asmir Begovic was forced to parry away Ozil's dangerous free-kick.
Geoff Cameron replied for Stoke in the 26th minute when he side-footed home from just inside the area before Per Mertesacker got on the end of fellow German Ozil's corner to send a looping header past Begovic.
The win was wrapped up with a little less than 20 minutes remaining when Bacary Sagna headed home another Ozil free-kick to have the Gunners sitting on top of the standings on 12 points, equal with north London rivals Tottenham, who needed an injury-time goal from Paulinho to beat Cardiff City 1-0.
Aston Villa returned to the winners list with a 1-0 result over Norwich City thanks to Libor Kozak's first goal for the club while Dejan Lovren's debut Southampton goal ended Liverpool's unbeaten streak as the Saints won 1-0 at Anfield.
Hull City came from behind on two occasions to stun Newcastle United 3-2 at St James' Park despite a Loic Remy double while West Bromwich Albion defeated Sunderland 3-0 at The Hawthorns, which brought about the demise of Black Cats boss Paolo Di Canio.
2013/14 Barclays Premier League scores