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.
Copyright by STATS LLC and The Associated Press
Arena: Wells Fargo Center Location: Philadelphia, Pennsylvania
Referees: Kelly Sutherland, Kyle Rehman Linesmen: Brad Kovachik, Tony Sericolo
Attendance: 19,360 (99.3% full)
Team Stat Comparison
Power Play Goals
Power Play Opportunities
Shots on Goal
Marek Zidlicky (2)
Assists: Ryane Clowe, Patrik Elias
No scoring this period
Mike Sislo (1)
Assists: Rod Pelley, Jacob Josefson
Kimmo Timonen (1)
(Power Play) Assists: Claude Giroux, Vincent Lecavalier