Only victory over the visitors would ensure survival, but they could only manage a 2-2 draw.
Alan Lee put Palace ahead in the first half, only for Leon Clarke to level matters just before the break. Palace went ahead again thanks to a second half Darren Ambrose goal, but the Owls fought back with a Darren Purse shot with just three minutes of normal time remaining.
Five minutes of injury time ensured a nervous end to the game but Palace, who had 10 points deducted this season for going into administration, managed to hang on.
Joyous Palace fans spilled on to the pitch at the final whistle prompting riot police to ensure both sets of fans were kept apart.
But any hint of trouble could not detract from the celebrations of 6,000 travelling Palace fans, who had been expecting a play-off challenge in January before administration plunged them instead into a relegation scrap.
Owls manager Alan Irvine envisaged this scenario when handed the task of ensuring the club's survival after replacing Brian Laws in January - and his worst fears were realised despite his side's valiant efforts.
The Owls made just one change, replacing striker Leon Clarke for midfielder Tom Soares, while Palace brought in Lee for the suspended Neil Danns, who was sent off against West Brom on Monday.
Owls fans missed a collective heartbeat in the third minute when Palace skipper Shaun Derry's inviting cross was fired straight at goalkeeper Lee Grant by Palace forward Calvin Andrew.
Andrew escaped with a yellow card in the 14th minute after his studs caught Grant full in the face, but the Owls goalkeeper recovered to keep out Darren Ambrose's fine free-kick at full stretch soon after.
But Grant was beaten when Ambrose swung over a corner and Lee towered above the home defence to crash his header high into the centre of goal.
Clarke and most of Hillsborough howled for a penalty after the big Owls striker was sent tumbling in the penalty area shortly before the break, but referee Mike Dean was unimpressed.
The moment Wednesday fans had been desperate for came two minutes before half-time.
Palace right-back Danny Butterfield made a hash of a long ball forward and was robbed out wide by Clarke, who raced in on goal at an acute angle and curled the ball home brilliantly inside Speroni's far post.
Clarke appeared to pay a heavy price for jumping the hoardings in celebration as he was stretchered off straight after the restart and replaced by former Palace midfielder Tom Soares.
Tempers flared in the tunnel as the players left the field at the interval, with so much hingeing on the final 45 minutes of the season, while Owls midfielder James O'Connor emerged for the second period with his head bandaged.
Midfield partner Darren Potter was next to leave the pitch to get a head wound cleaned following a challenge with Derry and he too reappeared bandaged up.
Wednesday pressed the visitors back and only a superb sprawling save by Speroni stopped Luke Varney giving the Owls a 59th-minute lead.
But it was Palace who broke the deadlock four minutes later. Sean Scannell weaved his way to the byline and cut the ball back for Ambrose to bury a low, right-footed shot beyond Grant.
Speroni charged bravely off his goalline to deny Soares another scoring chance for the Owls and Johnson headed a cross from substitute Etienne Esajas over the crossbar with 20 minutes remaining.
Nerves then began to tell for both sides before Purse raised the Hillsborough roof when his outstretched leg converted at the far post after 86 minutes.
Palace somehow scrambled clear another corner and then hit the post through substitute Stern John in a nerve-shredding finish.