GLENDALE, Ariz. -- Rasmus Dahlin scored his first NHL goal 2:45 into the game, and Linus Ullmark made 36 saves for the Buffalo Sabres for his first NHL shutout, a 3-0 win against the Arizona Coyotes at Gila River Arena on Saturday.
[WATCH: All Sabres vs. Coyotes highlights]
Dahlin, the No. 1 pick in the 2018 NHL Draft, pushed the puck into an open net to make it 1-0 after Jeff Skinner drew goalie Antti Raanta out of the crease to play a shot near the left post that deflected to Dahlin.
"I need to thank Skinner, when I saw the puck on the goal line," said Dahlin, who at 18 years, 183 days is the youngest defenseman to score a goal in Sabres history. "He made a great move to get open, a great move on the goalie too, and it was an open net."
Video: BUF@ARI: Dahlin nets a loose puck for his first goal
It was Skinner's first point with the Sabres.
The forward, acquired in a trade from the Carolina Hurricanes on Aug. 2, scored his first goal with them at 16:29 of the third period to make it 3-0, but he seemed more excited about Dahlin's goal.
"Rasmus made a real nice play getting it to me in transition and obviously a real good job following it up," Skinner said. "I should have put it in, but I was happy for him, his first one, his first of many. Pretty cool."
Coach Phil Housley moved Skinner to a line with center Casey Mittelstadt and right wing Kyle Okposo to help get him going after he was held without a point the first four games.
Conor Sheary scored on the power play at 18:06 of the first to give Buffalo a 2-0 lead. It was his third goal in four games.
The Sabres (3-2-0), off to their best five-game start since they went 4-1-0 in 2010-11, began a five-game Western Conference road trip. They were coming off a 6-1 loss to the Colorado Avalanche on Thursday, when No. 1 goalie Carter Hutton gave up all six goals.
Video: BUF@ARI: Skinner tucks sweet backhander under the bar
"Buffalo had to travel east to west, and I thought we could have jumped on them," Coyotes coach Rick Tocchet said. "We've got to score goals. To win in this league, you've got to score. I'm worried about the team in this situation … good teams know they're going to win, and some of our guys were a little sluggish early."
Raanta made 20 saves, but the Coyotes (1-3-0) couldn't follow up on a 3-2 shootout win at the Anaheim Ducks on Wednesday and haven't won two straight games in October since 2015.
Arizona, which outshot Buffalo 36-23, had at least 30 shots on goal in each game but has been shut out in three of four games to start the season, including two at home.
"We have a lot of shots, but I don't think we have those second and third (shots), we don't get rebounds like that," Raanta said. "Even though their goalie played a great game, we are making the goalies look really good right now. I think we have to get more of that eye of the tiger in front of the net and put those pucks in."
Ullmark, making his 25th NHL start and first of the season, made several difficult saves in the second period, when most of the Coyotes' nine shots were high-quality attempts from close to the net.
"It's always fun to make saves, especially if you can make enough saves for the team to win," Ullmark said. "They had some pushes, but we played real solid defensively. We were keeping the guys outside."
Video: BUF@ARI: Ullmark robs Panik with tremendous save
They said it
"You watch him play, you know it's going to come for him. He's got so much skill, it's nice for him to get it out of the way. I thought he played a great game, and it's only five games into his career. It's going to be fun to watch him, and it's going to be for a long time." -- Sabres forward Jeff Skinner on Rasmus Dahlin scoring his first NHL goal
"It's four games in and I know everyone's frustrated, everyone's frustrated we're not scoring goals. You're trying your best to figure it out, but at the end of the day, you've got to be able to will yourself a goal." -- Coyotes coach Rick Tocchet
Need to know
Sabres center Jack Eichel had an assist on Sheary's goal and has three goals and two assists in his past four games. … Buffalo is 8-2-1 in its past 11 games against Arizona and 9-2-0 in its past 11 at Gila River Arena. … The Coyotes outshot the Sabres 13-5 in the third period and have a 57-19 edge in that period this season. … Arizona plays its next four games on the road. … The Coyotes have been shut out in four of five games dating to last season.
Sabres: At the Vegas Golden Knights on Tuesday (10 p.m. ET; ATTSN-RM, MSG-B, NHL.TV)
Coyotes: At the Minnesota Wild on Tuesday (8 p.m. ET; NBCSN, NHL.TV)
Video: Dahlin scores first career goal in 3-0 Sabres win