The game was scoreless heading into the third period, but Jeff Carter scored just 18 seconds into the stanza and Danny Briere added a goal with 8:33 to go. Both goals came on the power play, Carter producing his 26th of the season and Briere scoring his 27th.
Tuomo Ruutu brought the Hurricanes within one with 7:53 left, but Boucher, who has split time this season with rookie Sergei Bobrovsky, was perfect the rest of the way while improving his record to 13-6-2.
Cam Ward stopped 23 shots for Carolina, which has lost four of its last five. The Flyers maintained a three-point lead over Pittsburgh at the top of the Atlantic Division.