Gylfi Sigurdsson’s delightful first-half volley secured a 1-0 victory and took Swansea to the points total generally regarded as enough for top-flight survival.
Sigurdsson’s strike, equalling Wilfried Bony’s record of 25 Premier League goals for Swansea, also inflicted a first league defeat on Chelsea since Guus Hiddink took over as interim manager in December.
Chelsea won 5-0 at Swansea last season on their way to the title, but there were only three survivors from the side which produced one of the real high points of Jose Mourinho’s second spell in charge.
Goalkeeper Thibaut Courtois gave way to Asmir Begovic while Chelsea’s roll call of absentees included John Terry, Gary Cahill, Nemanja Matic, Willian, Diego Costa and Loic Remy.
Chelsea looked dangerous when Oscar’s intelligent runs went untracked, the Brazilian setting up Ruben Loftus-Cheek to fire straight at Lukasz Fabianski before the young midfielder was foiled at the near post by Federico Fernandez’s timely intervention.
But the Chelsea defence was an accident waiting to happen with Ecuadorian winger Jefferson Montero, who had not started in the league since Boxing Day, tormenting them in the same fashion as he had at Stamford Bridge on the opening day of the season.