Derick Brassard and Sean Couturier scored for the Flyers (6-2-2), who are 4-1-1 in their past six games.
Jones has won three straight starts to begin his first season with Philadelphia.
"I feel good," Jones said. "The team's playing well. We're defending really well, and the penalty kill's been good. That's a good recipe for success for a goalie."
Brett Leason scored for the Capitals (5-2-4), and Vitek Vanecek made 30 saves.
"I thought in all three zones they were just quicker than us," Washington coach Peter Laviolette said. "When your opponent is quicker than you in the defensive zone, you're going to give up shots, you're going to give up zone time. … We just needed to be better."
Capitals forward Alex Ovechkin remains one goal from tying Brett Hull (741) for fourth in NHL history.
Brassard gave the Flyers a 1-0 lead at 11:18 of the second period when he scored on a one-timer from the left face-off circle off a pass from Cam Atkinson from below the goal line.
"The one thing we talked about this morning is that we're not going to score every game, but we've got to be effective," Brassard said of his line with Atkinson and Joel Farabee. "We're not a one-line team, we're a four-line team, and since the beginning of the season, everyone's chipping in offensively."