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's a winner. We want winners here, and he's a proven winner. He's won two Stanley Cups. He's 22 years old and been a big part of it. He's got all the right tools. He's got size (6-foot-1, 204 pounds) and strength. He's exactly what we were looking for. He's going to be a big piece of our team for many, many years to come.
— Blue Jackets GM Jarmo Kekalainen on Brandon Saad, who he acquired in a trade with the Blackhawks on Tuesday