Didier Drogba and John Terry looked to have snatched victory from the jaws of defeat with goals in the final six minutes - but the hosts' poor defending cost them when Clark nodded home a late equaliser.
Both sides had held the lead in an exciting game, with Frank Lampard's penalty cancelled out by Ashley Young's spot-kick and Emile Heskey's header giving Villa the lead.
The result left Chelsea marooned in fifth place, six points behind Manchester United having played a game more, and crucially outside the Champions League places.
That will place manager Carlo Ancelotti's position under fresh scrutiny, while opposite number Gerard Houllier may enjoy some respite after ending a run of six defeats in seven games.
Chelsea began the match buoyed from ending their worst set of results for 11 years in Wednesday night's ugly 1-0 win over Bolton.
But for all their early possession, they once again lacked any real penetration.
Jeffrey Bruma - making his full Premier League debut - saw a header from a corner blocked but the better chances all fell to Villa, with Gabriel Agbonlahor, Ashley Young and Stewart Downing all going close.
But a sudden loss of discipline cost them dear, captain Stiliyan Petrov booked for a stupid lunge on Florent Malouda moments before James Collins climbed all over the Frenchman to concede a penalty.
Malouda did throw himself to the floor, and Brad Friedel and Collins were both cautioned for protesting, but it was a definite foul and Lampard stepped up to convert his first goal since August.
Villa's frustration got the better of them and they were penalised for more than one late tackle, while Reo-Coker, Agbonlahor and Clark were all booked before half-time.
Clark and the recalled Richard Dunne both missed glorious chances to level when they headed and hooked over, respectively, from close range as Chelsea's defence went to sleep.
Dunne also produced a last-gasp tackle to stop Malouda and a vital clearance to thwart Michael Essien.
Ramires was booked for clipping Petrov's heels and Villa's pressure finally told when Essien's clumsy tackle on Reo-Coker handed them a penalty four minutes before the break. Young made no mistake from the spot.
Collins nodded another half-chance too close to Petr Cech before half-time and Villa picked up where they had left off right from the restart.
And Heskey put them ahead just two minutes in when he climbed above young Bruma to power home Downing's excellent right-wing cross.
The former England player was then booked for a late tackle on Essien as Chelsea began to wake up to their predicament.
Lampard, Drogba and Ramires all saw shots blocked before the latter drilled just wide after the ball broke to him in the box.
The weakness of Ancelotti's bench was summed up when he sent on Jose Bosingwa for Paulo Ferreira.
Lampard was unlucky not to level in the 63rd minute when he sent a vicious volley straight at Friedel, who then brilliantly closed down Malouda as the forward tried to slot Lampard's ball through the keeper's legs.
Ancelotti threw on Salomon Kalou for Ramires for the final 17 minutes.
Downing drilled straight at Cech from 25 yards before Terry was carded for a lunge on Young and Ancelotti played his final card by introducing Daniel Sturridge for Nicolas Anelka.
Chelsea were denied in the final 10 minutes by some desperate Villa defending as the visiting fans began to chant, "You're getting sacked in the morning!", at Ancelotti.
But Drogba came to his manager's rescue six minutes from time with the ugliest of equalisers.
The struggling striker's miscontrol set up Kalou, whose shot was blocked back for Drogba to rifle home via Carlos Cuellar.
Drogba then nodded over Malouda's corner after Villa had brought on Marc Albrighton for an injured Agbonlahor.
With barely a minute remaining, Chelsea snatched what they thought was a winner.
Drogba's bullet header was parried by Friedel straight to Terry, who produced a superb sidefoot finish to spark wild celebrations, with Ancelotti mobbed by his own players.
But the joy was short-lived, with Clark stealing in completely unmarked at the back post to nod in Albrighton's cross.
There was still time for Drogba to volley Bosingwa's cross wide and Albrighton to mishit a volley as both sides poured forward in search of a winner.