The Flames outshot the Leafs 15-7 in the first period but Jonathan Bernier held them off the board.
James Van Riemsdyk scored a short-handed goal late in the first period.
Matt Stajan scored his first of the year late in the second stanza, cutting the Leafs lead in half after 40:00 of play.
The Glencross-Stajan-Jones line combined for 12 shots through two periods. The Flames had 35 in that span while the Leafs had 15.
David Jones scored his third of the year in the third period.
The game featured two fights. Brian McGrattan was in his first fight of the year, picking up a win over Frazer McLaren. Shane O'Brien dropped the gloves with Carter Ashton after the Leaf slammed Derek Smith into the boards.