City goalkeeper Costel Pantilimon, again preferred to Joe Hart, had earlier saved twice from Jonjo Shelvey.
Hart might have hoped to feature after playing in the Champions League in midweek but, aside from Joleon Lescott replacing the injured Matija Nastasic, City fielded the side that thrashed Tottenham 6-0.
City again raced out of the blocks with Sergio Aguero charging through and shooting at Gerhard Tremmel inside the first minute.
Tremmel was quickly in action again as Negredo forced him to tip around the post with a long-range shot.
Negredo was fouled outside the area shortly afterward and stepped up to clip home the resulting free kick in the eight minute.
Swansea then enjoyed a spell of dominating possession and creating a couple of chances, with Shelvey twice forcing Pantilimon to save with shots from distance.
Both sides had penalty appeals as Pablo Hernandez claimed to be pulled back by Martin Demichelis and Aguero went down under a Jose Canas challenge but referee Mark Clattenburg was convinced by neither.
De Guzman shot at Pantilimon and spurned an even better chance to equalize when he fired over just before the interval
City's second finally came just before the hour as Yaya Toure strode forward in trademark fashion to find Nasri inside the area. The Frenchman still had much to do but the defense could not touch him as he ran across goal and fired low into the bottom left corner.
City almost had a third when Toure found Aguero and Swansea's half-clearance fell to the inrushing Pablo Zabaleta but the fullback shot over.
But there was little respite for the Swans and Zabaleta instead turned to a creator's role by rushing onto a James Milner throughball and pulling back for Nasri to tuck home after 77 minutes.
The former Arsenal playmaker, sensing a hat trick, curled just wide and Fernandinho shot over in the closing moments.
