Ashley Cole was red-carded as last-gasp equaliser 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 second half 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.
Swans boss Brendan Rodgers made 10 changes to his side following their FA Cup exploits at the weekend with just Ashley Williams remaining from the XI that started against Bolton.
Chelsea boss Villas-Boas again decided against giving Gary Cahill his full-debut with the £7 million man starting on the bench. Branislav Ivanovic played in central defence in place of the injured John Terry.
The home side started the match well, quickly settling into their usual rhythm and maintaining possession well in midfield, as 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, when 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 Angel Rangel's through ball found Graham who turned Ivanovic well but was foiled by Cech when one-on-one, before the ball fell to Sigurdsson who saw a shot blocked. Graham's follow-up was then cleared off the line by Luiz before a fourth effort by Joe Allen was saved by Cech and the Blues continued to live a charmed life.
Shot in the foot | Neil Taylor's own-goal snatched victory from the home side
The Swan's continued to threaten, however, with 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 to save.
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.
Chelsea had staggered through the first-half and failed to create a chance to equalise before half-time, but saw Cole and Florent Malouda booked for clumsy challenges on Sigurdsson and Leon Britton respectively.
Villas-Boas looked far from impressed as the side's went in for the break and his team came out for the second period with more vigour to their play as they pushed Swansea back into their half but still they struggled to penetrate the Swans' backline, as Williams and Caulker dealt comfortably with the forlorn Fernando Torres.
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, Kemy Agustien coming on for the tiring but otherwise impressive Sigurdsson.
The Blues were looking ominous and Bosingwa tested the home side's defence with a superb run and cross from the right, but Rangel kept calm to clear the ball with a header before Vorm gathered Caulker's deflection from Meireles' follow-up.
The Portuguese full-back was becoming Chelsea's main source of attacking threat as he again surged forward and found Sturridge inside the penalty area - the former Manchester City man turned neatly away from his marker but could only toe-poke the ball agonisingly past the post.
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.
The Blues were rewarded for their 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 hapless Taylor.