Swansea had impressed after falling behind to an early Alvaro Negredo free-kick at the Etihad Stadium but Nasri's double ended their spirited resistance.
Nasri, arguably enjoying his best spell of form since joining the club, went close to a hat-trick when he curled an effort wide five minutes from time.
Victory lifted City to third in the table and maintained their 100 per cent home record.
Chelsea bounced back from conceding a Jay Rodriguez goal after 13 seconds to beat Southampton 3-1 and move within four points of Barclays Premier League leaders Arsenal.
Michael Essien, making his first league start of the season, was at fault for Saints' goal and was hooked at half-time with his side still behind.
Goals after the break from Gary Cahill, John Terry and substitute Demba Ba earned Chelsea's sixth home win from seven games this season to extend Jose Mourinho's unbeaten Premier League record at Stamford Bridge to 67 games.
Liverpool lost ground on the table-topping Gunners as strikes from Jake Livermore and David Meyler, as well as a Martin Skrtel own goal, handed Hull a 3-1 victory at the KC Stadium.
The Reds were without the prolific Daniel Sturridge as he began what could be a stint of up to eight weeks on the sidelines after suffering ankle ligament damage in training on Friday.
Livermore put Steve Bruce's side ahead after 20 minutes when his shot from outside the area took a deflection off Skrtel past Simon Mignolet.
But the Reds were back level seven minutes later when skipper Steven Gerrard curled a free-kick around the wall into the net.
Meyler then scored with 18 minutes remaining to give the initiative back to Hull and Tom Huddlestone's shot was headed into his own goal by Skrtel with three minutes remaining to hand the Tigers victory.
Premier League
1 Arsenal 31
2 Chelsea 27
3 Man City 25
4 Liverpool 24
5 Everton 24
6 Newcastle 23
7 Southampton 22
8 Man Utd 22
9 Tottenham 21
10 Hull City 17
11 A Villa 16
12 West Brom 15
13 Swansea 15
14 Norwich 14
15 West Ham 13
16 Stoke City 13
17 Cardiff 13
18 Fulham 10
19 Sunderland 8
20 C Palace 7
Manchester United striker Wayne Rooney scored twice to deny Tottenham victory in a 2-2 draw at White Hart Lane.
Kyle Walker scored a free-kick to put the hosts ahead in the first half, but the England right-back haplessly set up Rooney for Manchester United's equaliser on the half hour.
Spurs chief Andre Villas-Boas thought he had gained a much-needed win when Sandro's 25-yard screamer sailed past David De Gea, but Rooney scored a crucial penalty to make secure a point.