Rielly took a feed from Toronto captain John Tavares on a 2-on-1 to beat Montreal goalie Carey Price and end a chaotic extra period where both teams had chances to get the victory.
“Those OTs, it really comes down to breaks,” Rielly said. “They had a breakaway moments prior to that, that was probably my fault.
“You win some, you lose some.”
William Nylander had two goals and an assist for Toronto, while Tavares added a goal and two assists. Jimmy Vesey chipped in with his first goal for the Maple Leafs, and Frederik Andersen had 28 saves.
Josh Anderson scored twice in his debut for Montreal, while Nick Suzuki had a goal and an assist, and Tomas Tatar also scored. Jonathan Drouin and Jeff Petry each added two assists inside an empty Scotiabank Arena because of COVID-19 restrictions.
“To start the season off in Toronto is pretty special,” said Anderson, who grew up in nearby Burlington, Ontario. “We wanted to get the two points, but it’s a long year.”
Price finished with 29 saves in the first of 10 meetings between the clubs.
“Not too excited, they’re hard games,” Rielly said with a grin when asked if he was looking forward to nine more games against Montreal. “We’re going to play them nine more times, and we’re going to play hard. I would expect the same out of them.
“It’ll be entertaining to watch, to be a part of.”
After the Leafs erased a two-goal deficit late in the second period, Anderson got his second of the night 1:03 into the third by cutting around Tavares and firing a shot that beat Andersen under his right arm to make it 4-3.
The Toronto goalie then denied Anderson his first-career hat trick on the doorstep a few minutes later after Suzuki stepped past Rielly.
One of the Leafs’ lesser-known offseason additions, Vesey took advantage of a fortuitous bounce with 10:33 left in regulation when Drouin’s clearing attempt hit one of the referees in the corner. Nylander jumped on the loose puck and quickly fed Vesey, who beat a surprised Price.
Auston Matthews, who scored in his four previous openers, followed that up by ripping a shot off the post behind the Montreal goalie that stayed to set the stage for overtime.
Toronto, Montreal and Canada’s five other NHL franchises are playing in the North Division necessitated by border regulations related to non-essential travel.
The teams hit the ice in front of more than 19,000 empty seats — Canadian fans, and those in most NHL cities, aren’t allowed into arenas at least to start — tarps mostly adorned with corporate sponsors covered the first six rows, and coaches wore league-mandated mask behind the benches.
“We’re just grateful to be playing,” said Rielly, now in his eighth season with the Leafs. “We’re going to have the most fun with it we can.”
After some nice saves from Andersen and Price, Montreal opened the scoring at 12:49 on its second power play when Suzuki scored from a tight angle after Jonathan Drouin tipped Petry’s point shot off the post.
Toronto replied 3:07 later when Nylander worked a give-and-go with Justin Holl and wired a one-timer past Price through a screen.
But the Canadiens retook the lead late in the period when Anderson, acquired from Columbus in the Max Domi trade before signing a seven-year extension, opened his account with his new team from the slot off a feed from Drouin.
Wayne Simmonds had a great chance to get Toronto level early in the second, but hacked a loose puck wide of an empty cage.
Montreal went back on the man advantage and after Andersen stopped Drouin in alone, Tatar got another breakaway and beat the Leafs’ goalie between the pads off a feed from rookie defenseman Alexander Romanov at 7:20.
The tough-as-nails Simmonds dropped the gloves with Montreal’s Ben Chiarot later in the period, scoring a victory in his first fight with his hometown club.
“That was a turning point,” Nylander said. “He got the boys going, fired up. We were a little soft and slow in the beginning.”
The Leafs made it 3-2 with two minutes left in the period on a man advantage when he roofed another shot on Price after Edmundson broke his stick.
Toronto went right back on the power play when Suzuki went off for hold before Montreal captain Shea Weber fired a clearing attempt off the ensuing faceoff over the glass for a delay-of-game penalty.
After the Leafs looked a little disjointed up two skaters, Marner fed Tavares in front and he deflected the pass through his legs to tie things with 38.7 seconds remaining.
Canadiens: At Edmonton on Saturday and Monday nights.
Maple Leafs: At Ottawa on Friday and Saturday nights.