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.
Gerhard Tremmel was preferred to Michel Vorm in goal for a Swansea team without Angel Rangel and Wilfried Bony due to respective calf and hamstring problems suffered during the 1-0 UEFA Europa League defeat to Valencia on Thursday.
Tremmel made early stops from Sergio Aguero and Negredo but was rooted to the spot when the latter opened the scoring.
Jose Canas brought down Negredo 22 yards from goal and the forward steered the resulting free-kick, from the right-hand edge of the penalty area, into the far corner, assisted by Lescott and Martin Demichelis peeling off the edge of the Swansea wall.
Swansea responded well and Jonjo Shelvey twice tested City goalkeeper Costel Pantilimon, who was again selected ahead of Joe Hart, from long range before Alvaro Vazquez dragged wastefully wide after 21 minutes, having been played in by the ex-Liverpool midfielder.
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.
The angle closed cruelly on Aguero as he hit the side netting in the 53rd minute after collecting a raking ball with an exquisite touch and rounding Tremmel.
Yaya Toure was the provider on that occasion and the Ivory Coast midfielder tore at Swansea with one of his trademark driving runs in the 58th minute before finding Nasri, who cut inside Ashley Williams and produced an assured finish.
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.
