With this win Manchester City moved smoothly into third place. Manuel Pellegrini's team have a test in Wednesday's trip to West Bromwich Albion but at home they cannot stop winning.
The record stands at a perfect seven victories and if City can overturn their miserable away form – four defeats and one win from six attempts – they will pose the greatest threat to Arsenal, who remain six points ahead of them.
Before kick-off Pellegrini had said: "I would like to arrive at the new year in first place but if that is not possible then no more than three points from the number one position." Afterwards he was asked if he was still confident of doing so. Referencing the upcoming trips to West Brom and Southampton, Pellegrini said: "I can answer your question when this week has finished, after the two games we are going to play away. I have a lot of trust in this team. We have six games in December. We hope we can do it."
On what awaits at the Hawthorns, he said: "It's a big challenge because they are a strong team at home."
In perhaps a clear signal that Joe Hart is going to endure a lonely festive period Costel Pantilimon was again Pellegrini's preferred choice. The two saves in quick succession from Jonjo Shelvey – each stretching his 6ft 8in frame to the right – suggested it may be a long wait for Hart.
Pellegrini said: "Costel Pantilimon did very well, he didn't have too much work but when he needed to be there he really did well."
Shelvey came close to creating his side's equaliser when he ran at the City defence before finding Alvaro Vázquez with a reverse pass that Swansea's lone striker should have finished.
Earlier Álvaro Negredo had claimed a 12th in 19 appearances for his new club. The Spaniard drew a free-kick when José Cañas clipped him, then stepped forward to thump it beyond Gerhard Tremmel.
At the end of the half Martín Demichelis, who had earlier headed against the Swansea bar, was deposited on his backside by the slick turn of Jonathan de Guzman but Swansea's midfielder blasted over.
The near miss, though, signalled the danger for City of sitting back and Pellegrini will have reminded his team during the interval of the need to wake up. He spent most of the second half prowling the technical area, hoping to see the further goals that would confirm his side's 100% winning record before their own crowd.
After 58 minutes the manager's mood brightened. Yaya Touré slipped in Samir Nasri who produced a finish of which Sergio Agüero would have been proud, zipping the ball past Tremmel before later adding a third with a similarly calm strike.
In response to Real Madrid's reported interest in buying Agüero in January, Pellegrini said: "I don't know anything about that. I don't think Sergio wants to leave. That is not a problem for us. I don't believe in that." His squad could be bolstered by the return of his captain Vincent Kompany, who has not played since 5 October owing to a thigh injury. "We will see [on Monday]. He works normally the last three days with the whole squad. Maybe he will be fit on Wednesday," said the manager.