Picard, who along with fellow rookies Jussi Timonen and Lars Jonsson made up half of Philadelphia's depleted defence corps, set up power-play goals by Randy Robitaille and Mike Knuble with long shots as the Flyers bounced back from a tough home loss to win for just the eighth time this season (8-15-3).
Simon Gagne scored a short-handed goal late in the second period and Antero Niittymaki made 39 saves in his sixth straight start for Philadelphia, beaten 3-2 by Nashville on Wednesday.
Chris Simon backhanded a shot past Niittymaki with 30.3 seconds left in the middle frame and Richard Park added a goal in the third, but it wasn't enough offence for the Islanders in their second game without injured leading scorer Alexei Yashin.
The Islanders, 0-2 without Yashin after a 6-1-1 stretch, have scored four goals since the captain sprained his right knee. Backup goalie Mike Dunham stopped 20 shots in place of starter Rick DiPietro, expected to play back-to-back nights this weekend at Pittsburgh and the New York Rangers.