Alex Auld stopped 17 shots and Anton Volchenkov and Chris Neil also scored for the Senators, who won their second consecutive home game. Auld, making his seventh straight start, improved to 5-2-1 in eight appearances overall.
"When things are going good, they're going good sometimes and you don't want to ask why," Heatley said. "I think overall, it starts with [Auld]. He's just solid for us, calm and solid back there, and then from there, we work on our defensive game. Overall, we're coming back, our D are moving the puck well and recently we're getting offensive contributions from everybody."
Mike Fisher had two assists after picking up his first two points of the season Tuesday night in a 2-1 win over Washington, including his first goal of the season in overtime.
Ottawa is 4-0-1 in its last five games following a four-game losing streak.
"They're playing well right now," Philadelphia coach John Stevens said. "You've got to give them credit. They played a sound hockey game and we've got to show more patience from start to finish to keep these games close early so we don't have to play catch-up all night."
Arron Asham scored his first goal for the Flyers, who lost their second in a row after a four-game winning streak and fell to 4-5-3 overall.
Philadelphia captain Mike Richards got his 11th assist on Asham's goal 7:18 into the second, which cut the Senators' lead to 2-1 before Winchester scored 56 seconds later.
"When we scored, I thought we had some momentum, and then they kind of crushed it there," Richards said.
Flyers backup Antero Niittymaki made 21 saves in his fifth start of the season.
Antoine Vermette appeared to have opened the scoring for the Senators 4:42 in, but a video review determined that the Ottawa left winger directed the puck into the net using his right skate in a distinct kicking motion.
"It's one of those calls that sometimes it goes your way, but it's a good thing we didn't need it tonight," Vermette said.
Volchenkov scored his second goal of the season at 8:49 when he put a slap shot from the right point past Niittymaki to give the Senators a 1-0 lead.
Heatley, a two-time 50-goal scorer with Ottawa, got his team-leading ninth goal during a power play at 12:42 after Philadelphia's Braydon Coburn was assessed a boarding major for driving Vermette into the boards with a check from behind in front of the Flyers' bench.
Asham drew Philadelphia to 2-1 when he put a shot over Auld's glove into the top right corner 7:18 into the second.
Winchester restored the Senators' two-goal lead 56 seconds later with his first goal in 14 NHL games overall, including each of Ottawa's 13 games so far this season.
"Both of my brothers were here and my cousin from Philly, actually, so it's pretty special," Winchester said.
Neil scored his second of the season into an empty net with 1:41 left in the third.
Asham, who has appeared in all 12 of the Flyers' games this season, had gone 33 regular-season games without scoring. His last goal also was in Ottawa on Feb. 18 as a member of the New Jersey Devils in a 3-2 loss to the Senators. ... Heatley has five goals and one assist during his five-game streak. ... Senators defenseman Filip Kuba recorded his team-leading 14th assist on Heatley's goal.