Gagne spent the first 10 years of his career with Philadelphia before being dealt to Tampa Bay for the 2010-11 season. He then went to Los Angeles, where he played one full campaign before being traded back to the Flyers on Tuesday.
Philadelphia already had a 2-0 lead when Gagne scored a power-play goal 3:54 into the second period.
Claude Giroux tallied just 23 seconds into the game and Wayne Simmonds scored on the power play to give the Flyers a 2-0 lead after one period. Maxime Talbot's slap shot also produced a Philadelphia goal with 5:05 to go in the second.
Braden Holtby started in goal for the Capitals, but was removed after giving up four goals on 18 shots. Philipp Grubauer came on to stop all 14 shots he faced.