Having absorbed much of Fulhams pressure, Palace punished rare lapses in intensity and concentration to score toward the end of each half through Jeffrey Schlupp and then Wilfried Zaha.
There was still cause for encouragement for Slavisa Jokanovics promoted team in the way it often outplayed the visitors at Craven Cottage on the banks of the River Thames. After spending more than 100 million pounds ($128 million) in the summer transfer window, Jokanovic handed full debuts to six new signings.
But four minutes before halftime, against the run of play, Palace took the lead. Andros Townsend exchanged passes with Patrick van Aanholt, whose throughball fed Schlupp and allowed the midfielder to turn and from the near post send an explosive finish into the top left corner, beyond goalkeeper Fabris reach.
Palace grew in confidence but the hosts still posed the greater threat and were unfortunate not to be awarded a penalty shortly after the hour when Mamadou Sakho clumsily brought down Schurrle.
Palace produced an almost immediate response when Christian Benteke nodded Wayne Hennesseys long kick toward Zaha to send him through on Fabri, who produced a reaction save from the forwards powerful strike.
It was Fulhams ambition that again exposed them, this time in the 79th minute when Aaron Wan-Bissaka won possession, countered and played in Zaha, who went to round Fabri and instead finished underneath him.