"It's pretty big," Simmonds said. "It felt a lot better that we got the two points. Obviously, it's nice to get it out of the way, but it's even nicer to get the two points. Not too happy with our performance, we've got a few things we've got to fix, but a good two points to start off the (four-game) road trip."
Rielly's shot deflected off Matthews and Flames defenseman Rasmus Andersson to make it 3-1 at 2:42 of the third period.
With the goal, Matthews has scored against all 30 other current NHL teams. He missed a 4-2 win against the Edmonton Oilers on Friday because of an upper-body injury.
"I felt like I made some good progress over the couple of days," Matthews said. "I came to the rink a little bit early, tested it out. It felt fine."
Tkachuk scored on the power play to cut it to 3-2 at 6:33.
"Tight game," said Flames forward Elias Lindholm, who assisted on Tkachuk's goal and has five points in a four-game point streak (two goals, three assists) to start the season. "Today they had the bounces and I didn't think we got to their net enough, but we've got to fix that on Tuesday."
Jake Muzzin gave Toronto a 1-0 lead at 7:46 of the first period with a wrist shot from the point that deflected off Calgary forward Dominik Simon.
"It's some unlucky bounces, but I think we're playing good," Markstrom said. "If we keep working hard in practice and keep working hard in games and doing the right things, hopefully these bounces are going to stop. We've just got to work a little bit harder and create our own luck."
Mitchell Marner assisted on Muzzin's goal to reach 300 points in the NHL. Among players to debut with the Maple Leafs, only Syl Apps (284 games) and Charlie Conacher (294 games), reached 300 points faster than Marner (307 games).
Monahan tied it 1-1 at 12:53 of the second when he banked his own rebound off Campbell. Monahan has scored a point in each of Calgary's four games (six points; two goals, four assists).