Devils defenseman Marek Zidlicky opened the scoring at 6:37 of the first period, dancing around Flyers defenseman 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 defenseman 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.