The goalkeeper made two late saves before Wilfried Bony sealed the points on his first return to the Liberty Stadium since leaving in January
Toure opened the scoring as his effort from the edge of the area deflected in off Ashley Williams before James Milner doubled City's lead following a swift counterattack.
Gylfi Sigurdsson pulled one back for the Swans just before half-time before Bafetimbi Gomis levelled matters after latching onto Ashley Richards' crossfield ball.
But Toure put City back ahead as he beat Lukasz Fabianski at his near post with a powerful drive, and after Joe Hart made two fine saves to deny Federico Fernandez and Gomis, Wilfried Bony made the points safe with a placed finish in stoppage time against his former side.
Toure returned to the Manchester City starting XI in place of Fernando, while Richards replaced the injured Angel Rangel for Swansea and Gomis came in for Ki Sung-Yueng, who has been ruled out for the rest of the season following knee surgery.
And the French striker was heavily involved from the off as he drew an early save from Hart before scooping over from a Jefferson Montero cut-back.
The visitors were almost caught out when Nathan Dyer robbed a ponderous Eliaquim Mangala of the ball in a dangerous area, but saw his eventual strike touched wide by Hart.
Sergio Aguero then had an effort correctly ruled out for offside, but Toure fired his side in front with a shot from just inside the box that deflected off Swansea captain Williams and snuck past goalkeeper Fabianski, who might feel he should have done better.
And City doubled their lead nine minutes before the break – Aguero taking out Richards with a clever pass before Milner cut inside Neil Taylor to guide the ball beyond Fabianski.
Swansea could count themselves unfortunate to be 2-0 down, but Sigurdsson buried a shot in the bottom right-hand corner on the stroke of half-time to reduce the deficit.
Fabianski had to be alert in the early stages of the second half as he kept out efforts from Mangala, David Silva and substitute Jesus Navas, while Jonjo Shelvey forced Hart into a diving save at the other end.
Gomis' leveller came courtesy of a delightful Richards ball over the top, which the frontman brought down superbly and fired across Hart.
Swansea's fightback was to garner no reward, though, as Toure sent City back in front with a low strike to the bottom right-hand corner, before Hart pulled off one of the saves of the season to keep out a Fernandez header and kept out another Gomis effort moments later.
Home fans afforded Bony a warm reception when he was brought on for the last five minutes, but the Ivorian responded by wrapping up the win in stoppage time, as Swansea's slim hopes of Europa League qualification fizzled out.