Emmanuel Adebayor, signed from Arsenal for 25 million pounds in the summer, kept up his record of scoring in every league match since his transfer by heading in what proved to be the winner after 30 minutes.
Portsmouth, who have now lost their opening four league games fell to the bottom of the table after Everton came from behind to beat Wigan Athletic 2-1 in the afternoon's second match to gain their first points of the season.
Leighton Baines clinched victory for Everton who moved off the bottom and up to 16th place with a penalty deep into stoppage time against his old club.
Paul Scharner had put Wigan ahead against the run of play with a diving header after 57 minutes before Louis Saha equalised for Everton with a simple header five minutes later.
Aston Villa, who were eliminated from the Europa League on Thursday, overcame Fulham, who qualified for the group stage of that competition, with a comfortable 2-0 win at Villa Park.
An own goal by Fulham defender John Pantsil after three minutes and a powerful 59th minute drive from Gabriel Agbonlahor gave Villa the points.
GREAT START
Manchester City continued their great start when Adebayor rose unmarked from a crowded penalty area to powerfully head home Gareth Barry's corner.
That proved enough to consign Portsmouth to another defeat and their worst start to a season for 55 years.
City rose to fourth in the table with nine points out of nine, three points behind Chelsea and Tottenham Hotspur who lead the table with 12 points from four matches and level with Manchester United who have nine points from four games.
Portsmouth are bottom with no points from their four games.
Villa's win, following their 3-1 victory at Liverpool on Monday, lifted them to eighth, while Fulham are 15th.
