The Etihad Stadium faithful might have had designs on a repeat of the recent 7-0 and 6-0 romps over Norwich City and Tottenham after Alvaro Negredo netted an eighth-minute free-kick, but Swansea more than matched Manuel Pellegrini's men in the first period and Jonathan de Guzman should have equalised on the stroke of the interval.
However, Nasri followed his midweek UEFA Champions League strike against Viktoria Plzen with two more, the second from a first-time finish that capped a sumptuous team move featuring James Milner and Pablo Zabaleta.
The result moves Pellgrini’s men into third, six points shy of leaders Arsenal, while Swansea lie 13th.
Joleon Lescott featured at centre-back in the absence of injury victim Matija Nastasic (calf) – the only change to the Manchester City XI that thrashed Tottenham seven days ago.
Demichelis thudded a header from Nasri’s 30th-minute corner against the bar but the former Bayern Munich centre-back's defensive display was far less convincing.
Having escaped punishment for pulling back Pablo Hernandez in his own box, Demichelis was nutmegged and left on his backside by De Guzman, who blazed the subsequent glorious chance over in the first half’s final minute.
Swansea started to feel the pace as the game entered its final quarter and City right-back Zabaleta burst forward to chip narrowly over, while Aguero flashed a shot across the goalmouth from Milner's throughball having failed to convert the substitute's cross.
Nasri's final flourish arrived in the 77th minute and City will now aim to address their troublesome away form in trips to West Brom and Southampton over the next six days.
