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.
He is, in my opinion, one of the best defensemen in the NHL and continuing to grow. I think his game, from an offensive standpoint, he continues to drive our offense... I think there's still tremendous upside for Oliver.
— Coyotes GM Don Maloney on defenseman Oliver Ekman-Larsson