Kolarov drove home from a tight angle to break the deadlock after 60 minutes of a compelling Barclays Premier League encounter at Goodison Park before substitute Nasri wrapped up victory in the closing minutes.
The result took City clear at the top of the table after three games of the campaign and rewarded them for another fluid attacking display.
But spirited Everton caused them problems throughout the game and went close to taking the lead themselves when Romelu Lukaku hit the bar from a free-kick.
City, looking much stronger in defence this season, held firm to record a third consecutive clean sheet and further vindicate manager Manuel Pellegrini’s offensive philosophy.
City again went straight onto the attack. David Silva tested Tim Howard from a tight angle in the opening minutes and Sergio Aguero combined with Jesus Navas before also shooting at the goalkeeper.
Howard then saved again from Silva before the Spaniard drilled a low cross into the box which Raheem Sterling narrowly failed to turn in.
Everton grew into the game with Ross Barkley drawing a good save out of Joe Hart and Lukaku rounding the goalkeeper to slot home before turning to see an offside flag raised.
Seamus Coleman drove another good chance wide for Everton before Sterling, jeered on his first return to Merseyside since controversially leaving Liverpool, had a low effort turned away by Howard.
The hosts went close again as Phil Jagielka headed narrowly over from a corner but they suffered a blow as 19-year-old left-back Brendan Galloway was hurt in a tackle on Bacary Sagna.
Galloway, who has impressed in the absence of Leighton Baines but was clearly identified as a potential weak link by City, tried to continue but soon realised the task was beyond him. He was replaced by another youngster in Tyias Browning.
Everton finished the first half strongly with Barkley and Tom Cleverley both winning free-kicks outside the area after being felled by Eliaquim Mangala and Fernandinho respectively. Barkley fired the first over but Lukaku clipped the top of the bar from the second.
City responded after the break with Silva thumping a shot against the post after being fed by Sterling.
Sterling then provided the telling pass as City took the lead on the hour, feeding Kolarov out wide as the Serbian timed his overlapping run to perfection. The angle was acute but his shot proved too powerful as it beat Howard at his near post.
City should have had a second soon after as Navas broke clear but the Spaniard delayed his shot too long, when he might have passed to Aguero, and Howard blocked.
Everton were not finished and Vincent Kompany needed to clear off the line from a Gareth Barry header moments after Hart had been troubled by a corner.
Nasri made certain of victory when he raced onto a neat flick from Yaya Toure to neatly lob Howard in the 88th minute.