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 got a chance to play a thousand games and that's pretty special to me. To get a thousand [points], it's a great accomplishment. I'm not going to hide my feelings, I'm proud of that. To do it on a win, do it on a goal, I think it makes it special.
— New York Rangers forward Martin St. Louis after scoring his 1000th NHL point on Friday