TORONTO -- It is rare in hockey that the only goal of a game is scored in the first minute of the first period.

The Maple Leafs did just that Sunday night. Zach Hyman scored 34 seconds into the game, and backup goaltender Curtis McElhinney made sure it stood up, making 41 saves in a 1-0 victory over the Edmonton Oilers.

According to the NHL, Toronto became the 10th team in league history to score an opening-minute goal and win 1-0. It was the second time in two nights.

The Columbus Blue Jackets defeated the Arizona Coyotes 1-0 on Saturday night with a first-minute goal.

McElhinney, who was playing in his fifth game of the season, made some spectacular saves for his sixth career shutout.

"It's nice to see the first shot go in for the team and get a lead," McElhinney said. "You're up 1-0 right away, so it was kind of a tight game after that. They poured it on in the second (period) pretty good."

He also had some help from the goal posts.

"Sometimes you get lucky, and tonight I think there was about four of them," McElhinney said. "I'll take those breaks."

He improved to 6-0-0 in his career against Edmonton.

The Maple Leafs (20-10-1) were without center Auston Matthews, who was sidelined due to an upper-body injury, but they still earned their third consecutive win. Both teams were coming off victories on Saturday.

"We knew we had to start on time and we did," Toronto coach Mike Babcock said. "I thought our goaltender was really good, our penalty-killing was outstanding, and in the end, we spent too much time in our own zone. But, it's a big night on a back-to-back and a big win for us."

McElhinney had some of his big moments of the game against Oilers center Connor McDavid, who was a force throughout the game. McDavid had a breakaway while killing a penalty during the second period, but the Maple Leafs goalie stopped him.

"Obviously, you can see him coming a mile away," McElhinney said. "When he's 200 feet away and starts building speed, it's just like a freight train coming. You know he has the ability to dipsy-doodle and walk right through guys, it's pretty impressive.

"I don't think I've seen anyone else like it. I think it's one of those things. Thankfully, I don't have to go 200 feet with him, I've just got to match him the last little way, and I did it tonight."

McElhinney also stopped McDavid with a poke check in the first period.

"I probably surprised myself more than anyone," McElhinney said. "I think if he gets on the other side of that net, he's probably going to score. It's just one of those things, it's a desperation move at that point."

McDavid said, "I thought for sure we were the better team, we deserved little bit better tonight. Credit to them, they played good defense and their goalie was hot. You don't get anything for being close, so it's disappointing. We should have at least scored one goal, maybe a handful. For a 1-0 hockey game, I thought it was pretty entertaining."

Laurent Brossoit stopped 22 shots for the Oilers (12-16-2).

"We didn't win, obviously, but we were happy with our game," Edmonton coach Todd McLellan said. "We worked hard, we were very competitive. Tonight, the puck wasn't going to cross the line for us, no matter what we did. Give credit to their goaltender and a couple of other situations where we hit posts or missed empty nets. You have one or two like that a year.

"The unfortunate thing is we're not in a situation where we can give up those points like we did tonight."

With a revamped first line because of the injury to Matthews, the Maple Leafs scored on the first shift when Hyman tipped in a point shot from Jake Gardiner for his sixth goal. William Nylander passed the puck back to Gardiner to earn the other assist.

The Oilers went on a five-on-three power play at 17:38 of the second when Toronto had simultaneous penalties -- Roman Polak for cross-checking and Mitch Marner for tripping -- but did not score. McElhinney produced some big saves during the Oilers' barrage.

"They missed some shots, we had good goaltending," Babcock said. "Our guys did a good job. I didn't like the five-on-three call, you've got to be sure when you put a guy down five-on-three, but that's life."

NOTES: Toronto C William Nylander moved onto the first line between LW Zach Hyman and RW Connor Brown after C Auston Matthews (upper-body injury) was scratched. Maple Leafs D Connor Carrick and RW Nikita Soshnikov also were not in uniform. ... Toronto G Frederik Andersen was given the night off Sunday after a 4-3 road win against the Pittsburgh Penguins on Saturday. ... Edmonton LW Nathan Walker, LW Anton Slepyshev and D Eric Gryba did not suit up. ... Toronto FC, winners of the MLS Cup on Saturday, was honored before the opening faceoff. ... Edmonton completes a three-game trip Tuesday against the Columbus Blue Jackets. ... The Maple Leafs will visit the Philadelphia Flyers on Tuesday.