City won with goals from Mario Balotelli, Adam Johnson, Vincent Kompany and James Milner against his former club and moved on to 22 points from their eight matches, two points clear of United. The last time City topped the table at this stage of a top-flight season was 34 years ago.
Chelsea beat Everton 3-1 in an evening kick-off to move to within a point of United in third place, while Liverpool stayed fifth.
City, without out-of-favour Carlos Tevez, the injured Sergio Aguero and with top scorer Edin Dzeko on the bench, were still far too strong for Villa, who suffered their first league defeat this season.
City manager Roberto Mancini told Sky Sports afterwards: "It's normal when you return after the international break that you have a problem at the start of the game, but after that we started to play very well."
Balotelli put City ahead with an overhead-kick after 28 minutes - his fourth goal in his last four games. Mancini said: "I hope Mario continues like this."
City had the match won by the 52nd minute, when they were 3-0 up, before Stephen Warnock pulled one back for Villa only for Milner to score with a brilliantly worked goal he started and finished.
City have now scored 27 goals in their opening eight matches, having won seven times and drawn once. They face United at Old Trafford next weekend.
In the lunchtime kick-off at Anfield, Steven Gerrard, making his first start for seven months, put Liverpool ahead with a 68th minute free-kick against United before substitute Javier Hernandez equalised for the champions with an 81st minute header five minutes after coming on.
Chelsea stayed third when they saw off Everton at Stamford Bridge with first-half headers from Daniel Sturridge and John Terry and a third after 62 minutes from Ramires.
Everton, who had drawn with Chelsea on their last five league visits to the Bridge and knocked them out of the FA Cup there last season on penalties, were largely outclassed. Their only bright spot was when Apostolos Vellios scored in the 82nd minute, less than 20 seconds after coming on as a substitute.
Bolton Wanderers moved off the bottom of the table when they ended a run of six successive league defeats with a 3-1 win at fellow strugglers Wigan Athletic, where they could even afford to miss a penalty through Kevin Davies.
Blackburn Rovers picked up only their fifth point of the season with a 1-1 draw at Queens Park Rangers, who are still looking for their first home win, but the point was not enough to keep Blackburn off the bottom of the table.
Heidar Helguson put QPR ahead after 16 minutes before Christopher Samba headed Rovers level eight minutes later.
Norwich City maintained their good start with a 3-1 win over Swansea City in a battle of two of last season's promoted teams at Carrow Road, while Stoke City beat Fulham 2-0 at the Britannia with Jon Walters and Rory Delap scoring in the last 10 minutes.
