The Cottagers produced an encouraging display in possession on their return to the top flight, but came unstuck against a street-smart Palace, who sat deep for much of the encounter and won out thanks to Schlupp's speculative first-half strike and a late counter-attacking goal finished off by Wilfried Zaha.
Fulham started proceedings at an impressive pace considering that manager Slavisa Jokanovic had inserted seven of his 13 summer signings straight into the starting XI.
The hosts moved the ball impressively through the middle at pace and Fulham's first chance was to fall to right-back Cyrus Christie, who collected from Tom Cairney before lashing down low towards Wayne Hennessey's bottom corner.
Fulham looked like the side operating with more enterprise and Cairney soon found another smart ball for the run of Ryan Sessegnon, whose adroit delivery across the face of goal almost found an unmarked Andre Schurrle, but for some standout recovering work from Patrick van Aanholt.
Schurrle enjoyed a bright debut out on the right as he then found Aleksandar Mitrovic in the centre of the box, who was able to pull free of James Tomkins and draw a save from Palace stopper Hennessey, who dived to his right to keep the Eagles in the game.
Palace were quiet going forward for much of the first period, although Fulham stopper Fabri was called into action on the half-hour mark and he made a fine save to deny the head of Christian Benteke, who had leapt brilliantly to meet an Andros Townsend cross from the right.
For all of Fulham's endeavour on the ball, the Cottagers were to find themselves behind in the 41st minute, as Schlupp collected from Van Aanholt before evading Calum Chambers and smashing a speculative effort in at the near post.
Fulham's defence looked on questioningly, but the fault clearly stood with stopper Fabri, who seemingly dived over the effort which gave Schlupp his first ever Premier League goal for the Eagles.
The second period continued with much the same pattern of play as the first, and Palace might have stung Fulham again against the run of play. A long ball forward saw Benteke head the ball down into space for Zaha inside the box, whose volley was kept out by the outstretched legs of Fabri.
The Cottagers continued to struggle with the final pass despite periods of encouraging possession, and it took an early cross from Joe Bryan to muster another chance for Mitrovic, but the frontman could only guide his glancing header straight into the arms of Hennessey.
Palace hedged their bets on sitting deep and the tactics paid off with 10 minutes remaining, as Aaron Wan-Bissaka established the perfect counter from inside his own half to help tee up the visitors' second of the afternoon.
The full-back raced forward straight at the heart of the Fulham defence before feeding Zaha beyond the last man, allowing the forward to send a deft finish beyond Fabri, who had made things easier by racing off his line in bemusing fashion to ultimately condemn his side to an opening-weekend defeat.
FULHAM (4-3-3): Fabri; Christie, Chambers, Le Marchand, Bryan (Vietto 71'); McDonald, Seri (Johansen 82'), Cairney; Schurrle (Kamara 61'), Mitrovic, Sessegnon
CRYSTAL PALACE (4-4-2): Hennessey; Wan Bissaka, Tomkins, Sakho, Van Aanholt (Souare 90'); Townsend (Kouyate 88'), Milivojevic, McArthur, Schlupp; Benteke (Sorloth 83'), Zaha