Diego Costa rescued a point for Chelsea as Swansea secured a 2-2 draw to end Antonio Conte's perfect start to the season as head coach.
Costa gave the visitors the lead at the Liberty Stadium in the 18th minute with his third goal of the season, as Chelsea went in search for their fourth win of the campaign.
Swansea turned things around after the break, with two goals in two minutes thanks to Gylfi Sigurdsson's (59) penalty and Leroy Fer's (62) opportunistic finish.
But Chelsea eventually rescued a point and ensured their unbeaten start to the season remained intact nine minutes from time as Costa, who was influential throughout the match, struck with an overhead kick.
The draw means Conte's side stay second but trail Manchester City by two points after their victory in the Manchester derby on Saturday. Francesco Guidolin's side move up to 13th in the table.
Guidolin made two changes to the Swansea side that lost 2-1 to champions Leicester last time out, with Neil Taylor and Ki Sung-yueng coming in for Wayne Routledge and Modou Barrow.
The changes prompted an adjustment in formation with Guidolin setting his side up in a 3-5-2 system, but it was the unchanged Chelsea, who named new signings David Luiz and Marcos Alonso on the bench, who started the brighter of the two sides.
Willian gave Lukasz Fabianski an early test, firing a powerful shot straight at the Poland international, who palmed the ball to safety.
Willian was proving a real handful for Swansea, but was again thwarted by Fabianski who showed excellent handling skills to claim the Brazil international's cross with Costa waiting to pounce.
Chelsea were rewarded for their excellent start in the 18th minute when Oscar brought down Federico Fernandez's poor header before teeing up Costa, who fired into the bottom corner.
Swansea were struggling to make any impact until Fernando Llorente teed up Sigurdsson, who curled an effort wide of Thibaut Courtois' far post.
Guidolin opted for a change in formation before the break, introducing Barrow for Taylor as Swansea reverted to 4-4-2.
But Chelsea could have doubled their advantage seconds later as John Terry flicked on Nemanja Matic's corner, but Costa fired wide from close range with the goal at his mercy.
Conte was becoming more and more frustrated by Chelsea's failure to score a second goal and Swansea eventually made them pay.
First, Sigurdsson levelled from the spot after Courtois brought him down with a rash sliding challenge; the Iceland international becoming Swansea's top Premier League scorer with 26 goals in the process.
Fer then profited after Gary Cahill, who thought he was fouled, was caught in possession with the Dutchman squeezing the ball past Courtois and over the line.
Oscar headed over from point-blank range as time ran out for the visitors, but Chelsea continued to push forward and were rewarded in the 81st minute when Costa converted Branislav Ivanovic's deflected shot in style with an acrobatic effort.
Player ratings
Swansea: Fabianski (7), Naughton (7), Fernandez (6), Amat (6), Kingsley (7), Taylor (5), Ki (6), Cork (7), Fer (8), Sigurdsson (7), Llorente (7).
Subs: Rangel (6), Barrow (7).
Chelsea: Courtois (5), Ivanovic (6), Cahill (6), Terry (7), Azpilicueta (6), Kante (6), Willian (7), Oscar (6), Matic (7), Hazard (7), Costa (8).
Subs: Fabregas (6), Moses (6), Batshuayi (N/A).
Man of the Match: Diego Costa