Ashley Cole was red-carded as last-gasp equalizer sees two points cruelly snatched away from the hard-working Swans who again impressed at home in the Premier League
Scott Sinclair had looked to win the game against his former club after an excellently volleyed opening goal in the first half.
Ashley Cole was sent off late in the game as Chelsea seemingly ran out of steam but Jose Bosingwa's cross was knocked in by Taylor to give Andre Villas-Boas' men a hard-earned point.
The home side started the match well, quickly settling into its usual rhythm and maintaining possession well in midfield, Gylfi Sigurdsson's free-kick caused problems for Chelsea's backline but Danny Graham could only bundle the ball wide under pressure from Ivanovic.
It took the men from west London almost 15 minutes to create an opening, David Luiz took off on a trademark surge forward and his left-wing cross found Daniel Sturridge who fired wide of Michel Vorm's left-hand post.
Swansea hit back as Rangel's through ball found Graham who turned Ivanovic well but was foiled by Cech when one-on-one, the ball fell to Sigurdsson who saw a shot blocked, Graham's follow-up was cleared off the line by Luiz before a fourth effort by Allen was saved by Cech and the Blues' goal continued to live a charmed life.
The Swans continued to threaten, Scott Sinclair breaking two tackles in midfield before laying the ball to Nathan Dyer but the former Southampton winger's 25-yard effort was easy for Cech.
The home fans were celebrating soon after though, as Sigurdsson's free-kick was weakly headed into the ground by Ivanovic and looped up for Sinclair who expertly hooked a left-footed effort over his shoulder and into the corner of the Chelsea net, the Liberty Stadium crowd erupted but the Swans' winger refused to celebrate the goal against his former club.
Villas-Boas looked far from impressed as the sides went in for the break and his side came out for the second period with more vigor to its play as they pushed Swansea back into its half but still they struggled to penetrate the Swans' backline.
Bosingwa saw a volleyed effort blocked as Chelsea continued to feed on scraps in front of goal before Michael Essien was brought on for the final 25 minutes, replacing the defensively minded Oriol Romeu.
The Ghanaian almost made a perfect impact on the game, hitting a rasping half-volley over the crossbar with Vorm well beaten.
Swansea had been against the ropes for almost the entire second half and Brendan Rodgers injected some fresh legs into his midfield, Kemi Agustien coming on for the tiring but otherwise impressive Sigurdsson.
The Blues were looking ominous and Bosingwa tested the home side's defense with a superb run and cross from the right, Rangel keeping calm to clear the ball with a header before Vorm gathered Caulker's deflection from Merieles' follow-up.
Ashley Cole saw a dangerous cross well cut out by Caulker before Bosingwa again went close for the Blues, cutting inside from the right and hitting a swerving effort over the bar.
The Blues' task was made much harder with five minutes remaining as Cole picked up his second booking after a lunging challenge on Dyer. The England left back will now miss Chelsea's match against Manchester United at the weekend.
But Chelsea was rewarded for its incessant pressure however, Bosingwa again the danger-man bursting into the box and seeing his cross flash past Vorm thanks to a deflection off the helpless Taylor.