Chelsea suffered the agony of a last-gasp equaliser when Swansea struck minutes from time.
Victor Moses scored his first league goal for the Blues but Pablo Hernandez curled a beautiful goal to earn the Blue a point at the Liberty Stadium.
The single point wasn't enough to put Chelsea back on top of therefore League ahead of Manchester United.
The Nigerian popped up at the far post to nod on a Cahill header on 61 minutes.
But the visitors succumbed to a sucker goal two minutes from time from the cultured right boot of Danny Graham.
The Blues drop off top spot after United defeated Arsenal earlier in the day and have 23 pints from their opening 10 fixtures.
The Swans had an excellent chance on three minutes but only the outstretched leg of Gary Cahill prevented Michu from latching onto an excellent Pablo Hernandez cut back inside the Chelsea penalty area.
The Blues first effort on goal, on 12 minutes almost resulted in a goal. A Hazard corner was headed on by Cahill but unluckily for the centre-back Leon Britton was in the far post to clear.
Michu failed to connect to a Hernandez cross a minute later, instead whacking his volley high and wide of Petr Cech's goal from 10 yards out.
The visitors second effort came on 18 minutes when Belgium midfielder Eden Hazard tried a speculative shot from 20 yards. Predictability, the ball sailed over Gerhard Tremmel's crossbar.
Fernando Torres almost made and scored on 25 minutes. firstly setting up Victor Moses on the right with a deft through ball. Moses then arrowed a byline cross which Tremmel flapped at, allowing Torres to race in but his weak header from 12 yards, while on target, was not strong enough to evade Tremmel who recovered quickly to snaffle the ball.
Chelsea had. Half chance for. Penalty with seven minutes of the half remaining when Hazard went down under a string challenge by Ashley Williams. however referee Kevin Friend simply ignored the plaintive plea.
Two yellow cards in quick succession for Swans's 'Britton and Chelsea's Cesar Azpilicueta might have suggested a spiky passage of play - far from that, just clumsiness by the pair of them in fact as the dour encounter dragged on.
Right on the strike of half-time, Torres found himself clear with a run on goal. Sadly for the Spain striker he had no pace to get clear and was quickly chased down.
Roberto Di Matteo decided to make a change at half-time, replacing Oriel Romeu with Ramires.
Hazard forced Tremmel into a low diving save five minutes after the restart as the Blues took command of possession.
A fine counterattack by the home side a later saw Chelsea's rearguard at full stretch.
And that's exactly what Cole needed to do to tap the ball out fora order, preventing Michu from latching onto Britton's seemingly decisive through ball.
But the Blues, in second place at the start of the match produced two fine prices of play.
The first, a Hazard curling free-kick on the hour seemed destined to see the 20-yarder bulge the back of the net, but Tremmel produced a wonder save to parry the ball away for a corner.
However from the resultant kick from Hazard, the ball ended up in the back of the net after Cahill rose above the melee and headed towards goal, Moses popped up to head the ball on into the back of the Swans' net from close range.
Swansea responded well to the setback and Cech needed to be alert to Jonathan de Guzman's curler from just outside the Chelsea area.
A dinking cross by substitute Nathan Dyer, on 73 minutes, turned into an effort on goal, which forced Cech into tipping the ball over the bar when it looked like it was going to dip over the goalkeeper.
With two minutes remaining, Swansea got their just deserts and levelled the match. While Chelsea decided to go on a spot of ball watching, they failed to notice Substitute
Danny Graham on the edge of their area. The midfielder show cool and cunning to curl an inch-perfect right-footer around a posse of
Blue shirts and beyond the hapless dive of Cech.
In all, it was a dour game which Chelsea did not deserve to lose but frankly did not enough to win.
Chelsea - Cech, Azpilicueta, Cahill, Ivanovic, Cole, Moses, Oscar, Hazard, Mikel, Romeu, Torres,
Subs - Turnbull, Marin, Sturridge, Ferreira, Bertrand, Piazon Ramires Swansea City - Tremmel, Williams, Britton, Michu, Hernandez, Routledge, Monk, De
Guzman, Rangel, Sung-Yueng, Davies
Subs. - Cornell, Tate, Graham, Dyer, Shechter, Tiendalli, Agustien
Ref: Kevin Friend