Manuel Pellegrini could be forgiven for wondering how Manchester City will cope without Yaya Touré and James Milner after goals from the midfield pair edged them closer to a second-place finish in the Premier League.
The Ivory Coast International put the visitors ahead with his 50th Premier League goal, and then restored their lead after Swansea had recovered from two goals down in an enthralling contest.
Milner had doubled City's advantage before Gylfi Sigurdsson and Bafétimbi Gomis brought the hosts roaring back into the game.
But Touré struck the decisive blow before substitute Wilfried Bony marked his return to Swansea with a late goal to end his old side's European aspirations.
Touré's agent has claimed it is “90 per cent certain” the former Barcelona man will leave City this summer and, even after a season where he has not been at his best, the midfielder underlined just how difficult it will be to replace his presence.
Milner, meanwhile, is out of contract and is about to confirm a free transfer to Liverpool, even though Pellegrini believes the Etihad is the best place for the 29-year-old.
The City manager said: “James can play 10 positions and always do well. It is a decision James must take at the end of the season as to what is best for his future.
“He is an important player for our team because he is an intelligent player, who can play in several positions and always gives 100 per cent.
“I can think that being at Manchester City is best for him, but it is important what he thinks. I want to keep him.”
City's opener had come against the run of play as Swansea came bounding out of the blocks. The best early chance fell to Nathan Dyer, when the Swans winger pinched the ball off the hapless Eliaquim Mangala, but was denied by a superb save from Joe Hart.
However, City began to find some fluency and, once Swansea had failed to heed the warning of Sergio Aguero having a goal ruled out for offside, the visitors took the lead.
David Silva teed up Touré to take a touch and find the net via a deflection off Ashley Williams, although the Swansea keeper Lukasz Fabianski may feel he should have done better than palming the ball into the net.
Milner netted the visitors' second 15 minutes later. Frank Lampard and Aguero led the break for the midfielder to beat Neil Taylor and fire past Fabianski.
Swansea desperately needed a response and they got it in the dying embers of the first half. Taylor seized on a loose ball and found Sigurdsson for the midfielder to take a touch and dispatch an powerful drive into the bottom corner.
Jonjo Shelvey forced Hart into a sprawling save early in the second half as the hosts were carried along by the momentum from the goal. But soon it was Fabianski who was the busier goalkeeper, twice denying substitute Jesus Navas and then keeping out an angled drive from the irrepressible Silva.
Swansea took full advantage of his good work to level matters in the 64th minute. Mangala was caught out by Jazz Richards' long ball, which Gomis expertly controlled before sending a volley past Hart.
Chances kept coming at both ends but it was Touré who showed the clinical edge as he held off Jack Cork to drive forward and fire a low shot into the bottom corner.
City still needed Hart to make two outstanding saves to keep out headers from Federico Fernandez and Gomis, before Bony put the game to bed via the inside of the post.
“It was a beautiful save at an important moment,” said Pellegrini of Hart's remarkable stop from Fernandez. “Joe has improved a lot this season and he can get even better as he has an open mind and works hard.”
Garry Monk, the Swansea manager, added: “Ninety-nine times out of 100 that is a goal, unfortunately that was the one. They were both unbelievable saves. The one from Federico was incredible.
“But I am proud of us as we showed we can go toe to toe with a top side after being criticised for how we played even though we won on Monday.”
Swansea Manchester CitySubstitutions: Swansea City Barrow (Dyer, 73), Britton (Shelvey, 78), Emnes (Sigurdsson, 83). Manchester City Navas 6 (Lampard, 59), Kompany (Fernandinho, 80), Bony (Toure, 85). – The Independent