Gordon was promoted from Lehigh Valley of the American Hockey League on Monday after Dave Hakstol was fired.
Hart, recalled from Lehigh Valley on Monday, is the sixth starting goalie for the Flyers this season; they're the first team in NHL history to start six goalies in the first 35 games of a season.
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"I was just trying to play my game and trust my game, focus on the things that have gotten me to this point and not do things that are out of my control or out of my comfort zone," Hart said.
James van Riemsdyk and Shayne Gostisbehere each had a goal and an assist for Philadelphia (13-15-4), which ended a four-game losing streak with its fourth win in 15 games (4-8-3).
"I think it's a big relief for everybody," said Gordon, who coached his first NHL game since Nov. 13, 2010. "The record over the last little stretch would be frustrating for anybody. Myself, you always want to start on the right foot. Carter, it was a real fair game for him to have as his first game, wasn't under a lot of duress. And the team to go through what it's had to go through coming in here ... I thought our energy level was great throughout. It was a good way to start."