The Premier League relegation battle intensified as the Swans were beaten 1-0 by Chelsea at the Liberty.
Cesc Fabregas' early strike was enough to sink the Swans, who finished the day just one point outside of the drop zone after Southampton's victory over Bournemouth.
Fabregas curled home in the fourth minute after being teed up by the lively Eden Hazard, with Lukasz Fabianski left helpless.
The hosts pushed hard for an equaliser late on, with sub Nathan Dyer seeing a penalty appeal turned down while Andre Ayew, Jordan Ayew and Tom Carroll went close.
Kyle Naughton, Alfie Mawson and Wayne Routledge all shot too close to Thibaut Courtois as the Swans threw everything at Chelsea.
But the Blues did enough to hold on for the three points in a game short of chances.
It leaves the Swans on 33 points - one above Southampton - with three games remaining.
Swans: Lukasz Fabianski, Connor Roberts, (Tom Carroll, 63), Kyle Naughton, Mike van der Hoorn, Alfie Mawson, Martin Olsson (Wayne Routledge, 81), Andre Ayew (capt), Andy King (Nathan Dyer, 58), Ki Sung-Yueng, Sam Clucas, Jordan Ayew.
Subs: Kristoffer Nordfeldt, Angel Rangel, Leon Britton, Renato Sanches.
Chelsea: Thibaut Courtois, Antonio Rudiger, Gary Cahill (capt), Cesar Azpilicueta, Victor Moses, N’Golo Kante, Tiemoue Bakayoko, Cesc Fabregas (Pedro, 81), Emerson, Eden Hazard (Willian, 80), Olivier Giroud (Alvaro Morata, 85).
Subs: Willy Caballero, Ross Barkley, Davide Zappacosta, Andreas Christensen.