Devils defenceman Marek Zidlicky opened the scoring at 6:37 of the first period, dancing around Flyers defenceman Erik Gustafsson and evading goalie Ray Emery before backhanding the puck in from behind the goal line.
Sislo scored a similar goal when he beat Andrej Meszaros and beat Emery low on his stick side.
The Flyers got with 2-1 when defenceman Kimmo Timonen scored on the power play at 18:29 of the third period.
Emery had 17 saves and Cory Schneider stopped 21 shots for New Jersey.
The teams will complete the home-and-home series Thursday night in Newark.
I loved being in the jerseys again and they worked some magic for us. It was weird in warm-ups, seeing No. 22 in that jersey and thinking he’s [Mike Gartner], and No. 8 reminds you of Danny Briere … every number had me thinking back to the guys who wore them and smiling.
— Coyotes captain Shane Doan on wearing Kachina-style throwback jerseys in a 3-2 victory against the Canucks on Thursday