Luke Moore strike seven minutes from time to secure victory for Brendan Rodgers, Roberto Mancini's men and drag the States by a single point.
Joe Hart denied Swansea the lead in the first half after making a save of a penalty, but mastered by Scott Sinclair cities lack their usual control and dynamic players such as David Silva and Mario Balotelli no fuses magnet for visitors to the life.
Active players throughout the match Swansea were rewarded when Moore rose highest to head Wayne Routledge cross to the net to give the home team win as Micah Richards had a late effort not allowed the Vietnamese.
Swansea address from the start and the match started brightly as they go in the game through its fluid. This pressure nearly paid off early as a good move Routledge has a good chance but his shot over the bar.
Swansea has launched a first opportunity to take the initiative when Routledge was felled in the area of Hart and referee Lee Mason was right on the site. Sinclair has a stutter before a penalty shot was saved easily tame Hart palms the ball away from goal.
Danny Graham, Swansea continue the momentum when he found space in the box after serving Stefan Savic, but the striker fired his entire effort.
The city could not create significant occasions in the first half the home team controlled the midfield, while Ashley Williams and Steven occlusion Balotelli scored offside. Tourists best efforts to create pieces and photographs of long-range, none of which Michel vorm difficulties.
The answering machine of the dominant position of Mancini Swansea in the first half strong by the time period immediately threatened by Sergio Aguero, who beat his mark before firing a shot vicious in Section criteria that goes just wide of the post .
Swansea quickly approaching fire and take the lead when Graham launched a ball into the face of goal that eluded the team.
The city became angry when Balotelli has been considered a foul inside the area by Joe Allen, but the referee stopped the game Mason, leading to protests from Nigel de Jong and Yaya Toure in the field and Mancini, at the border.
The visitors began to get a grip on the game with David Silva to become more involved and Richards found his ball twists and turns in the area before making a great effort was saved by vorm goal.
Swansea, but remain strong in defense and were rewarded for their play when they took the lead on 83 minutes when Moore went Routledge cross in the corner beyond the chain Hart after an error by Gael Clichy.
Richards thought he won a point in the closing stages of the city, when he headed the ball into the net as vorm and missed Clichy cross, but while celebrating, Sian Massey raised his flag to rule out the goal.
Defeat ended his city four-game winning run in the tournament, and their reign as Premier League leaders, while in Swansea has shown why there is no reason to fear the fall of the season.