The Eagles, docked 10 points and still in administration, knew a win over promoted West Brom would be enough to keep them up and condemn Sheffield Wednesday to relegation.
Instead, they must head to Hillsborough on Sunday for a final-day decider in which they must avoid defeat to ensure survival.
Hopes were high at a raucous Selhurst Park after Steven Reid's own goal put the hosts ahead, but Albion defender Gabriel Tamas spoiled the party by equalising and clearing a last-gasp goalbound shot from Darren Ambrose.
Wednesday manager Alan Irvine was watching from the stands and headed back up the M1 safe in the knowledge his side's fate is back in their own hands.
Palace will only need a point to survive, but they will have to earn it without midfielder Neil Danns, who was shown a late red card for aiming a headbutt at Graham Dorrans.
Albion boss Roberto di Matteo played his strongest side and they had the ball in the net in the 13th minute, but Simon Cox had clearly punched it past Palace keeper Julian Speroni and the effort was ruled out.
The hosts were given another helping hand four minutes later when Ambrose swung in a free-kick and Reid inexplicably turned the ball past Scott Carson for the opening goal.
However, the lead lasted just four minutes and this time it was Palace who switched off at the back, allowing Tamas to bury a near-post header from former Wednesday winger Brunt's free-kick.
Calvin Andrew should have put Palace back ahead on the half-hour when Carson saved from Danns.
The ball looped across goal towards Andrew, but with the keeper scrambling and the net gaping, he put his header wide.
Palace were hanging on towards the end of the first half and Roman Bednar headed against the crossbar, while Speroni denied Cox and Brunt in quick succession before clawing away a dipping 30-yard volley from Graham Dorrans.
Palace's Argentinian keeper was back in action after the break, bravely blocking Robert Koren's blast and getting a vital hand to the ball as Bednar attempted to round him.
Eagles boss Paul Hart, knowing a point made no difference to his side's fate and desperate to avoid that last-day drama, threw on two extra strikers in Alan Lee and Stern John.
But try as they might Palace could not find the winner with Carson saving superbly from Ambrose and Lee, and Paddy McCarthy heading into the side-netting.
Danns' evening came to a premature end following his tangle with Dorrans, and with the final kick Tamas scooped away Ambrose's shot to ensure the agony goes on at the foot of the table.