Adam Wharton’s pass found Schlupp outside the box in the closing stages, with the substitute’s powerful effort arrowing into the top corner to leave goalkeeper Bernd Leno helpless.
Rodrigo Muniz’s thumping header had put Fulham in front shortly after the break.
The Brazilian got on the end of Timothy Castagne’s pinpoint cross as he continued his fine form since the end of January.
But Palace, now four matches unbeaten in the league, showed fighting spirit to come back with minutes left to play, after being the better team in the first half.
It looked like the visitors could end up punished for their profligacy in front of goal when Chris Richards headed an Olise free-kick over the bar, while in-form Jean-Phillipe Mateta volleyed high over the bar from close range.
Fulham’s best chances before the break came when Muniz almost caught Dean Henderson out at his near post and Issa Diop headed over from the resulting corner.
Marco Silva’s side had a record of eight home wins from eight in the Premier League when scoring the opening goal this season before Schlupp stunned Craven Cottage late on.
The hosts took the lead against the run of play and a draw was a fair result for two sides who are safe in the league for another season.
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Andreas Pereira played a ball across the box into the path of Bobby De Cordova-Reid but the forward shot high over the bar as the home side tried to build on Muniz’s opener.
Alex Iwobi, who became the fourth Nigerian player to make 250 top-flight appearances, provided a cutback for Harrison Reed who fired over the bar as Fulham missed a chance to double their advantage before Palace’s leveller.
Schlupp came on for Jordan Ayew with 14 minutes remaining and scored his second league goal of the season, 175 days after his first, to ensure Palace were rewarded for their performance.
Oliver Glasner’s side have been playing great attacking football of late, this their 11th goal in five league games.
Olise and substitute Odsonne Edouard also had low shots saved by Leno as the Eagles continued to apply pressure after the break.
Glasner’s side will be in confident mood when they host Manchester United on 6 May (20:00 BST).
