The Maple Leafs took a 1-0 lead at 18:31 of the first period when Spezza scored for a second straight game, shooting over Rittich's glove from the bottom of the left face-off circle.
"It's important you have depth on your team, and in games like this sometimes you need your depth to step up and get some goals," Spezza said, "but I thought more so we all defended really well as a group tonight."
Toronto outshot Calgary 11-5 in the period.
"I don't think we gave up very much in the first period, so to get out of it up 1-0 was really important," Maple Leafs coach Sheldon Keefe said.
Hyman made it 2-0 at 16:28 of the second period when he carried the puck around the Flames net and shot over Rittich's left pad. Alex Galchenyuk assisted on the goal for his first point with the Maple Leafs.
"It was incredible, it was a huge goal from Spezza to kick things off for us," Campbell said. "We were already playing a pretty solid first period and it was great to see, but anytime you can put the first one on the board, it gives the team a big spark. Hyman, he works so hard, I think everybody in the world knows that, and he led again tonight with his work ethic and got rewarded on the scoreboard, and I love seeing that for him."
NOTE: Andersen did not dress, and Hutchinson instead backed up Campbell. Keefe said after the game Andersen is dealing with the lower-body injury that caused him to miss four games from Feb. 22 to March 1.