Anton Khudobin made 25 saves for his first Stanley Cup Playoff shutout, and the Dallas Stars defeated the Vegas Golden Knights 1-0 in Game 1 of the Western Conference Final at Rogers Place in Edmonton on Sunday.
Khudobin (34 years, 122 days) is the 10th oldest goalie to get his first shutout in the playoffs.
"Mostly happy with the win," Khudobin said. "[The shutout is] a bonus I would say. Even if we win 2-1 or 3-2, doesn't matter. For me, the win is the most important."
[WATCH: All Stars vs. Golden Knights Highlights]
John Klingberg scored in the first period for Dallas, the No. 3 seed in the West, which entered having allowed 3.50 goals per game, the most of any of the four remaining teams.
"We knew the start of the game was going to be important tonight and I thought our team came out with a good effort," Dallas captain Jamie Benn said. "We played on our toes tonight and found a way to get one early there, and I thought [Khudobin] made a lot of great saves, especially in the third period. We found a way to squeak it out."
Game 2 of the best-of-7 series is in Edmonton, the hub city for the conference finals and Stanley Cup Final, on Tuesday (8 p.m. ET; NBCSN, CBC, SN, TVAS).
Video: DAL@VGK, Gm1: Klingberg strikes for early lead
The team that wins Game 1 is 488-221 (68.8 percent) winning a best-of-7 NHL playoff series, including 10-2 in the first two rounds this season.
Marc-Andre Fleury made 24 saves for Vegas, the No. 1 seed in the West, which was 0-for-4 on the power play. Fleury was making his fourth start this postseason and first since he made 28 saves in a 5-3 win against the Vancouver Canucks in Game 4 of the second round on Aug. 30. Prior to that, his previous start was in a 2-1 win against the Chicago Blackhawks in Game 3 of the first round on Aug. 15.
Robin Lehner, who started Vegas' other 12 postseason games, has three shutouts in his past six games, including a 3-0 win against the Canucks in Game 7 on Friday.
"I thought [Fleury] gave us the best chance to win tonight. He was fresh," Golden Knights coach Peter DeBoer said. "He's played well against Dallas (4-0-0 with Vegas prior to the loss) and he gave us a great game. I thought he was our best player. He gave us a chance to hang around when we didn't deserve to be in the game early."
Klingberg made it 1-0 at 2:36 of the first period, scoring on the Stars' first shot of the game from the high slot after Benn's initial attempt was blocked by Golden Knights defenseman Zach Whitecloud.
This is the only playoff game in NHL history to end 1-0 with the goal scored on one of the first two shots, and on the first shot by the winning team (since 1955-56).
"We came out of the gates strong," Stars coach Rick Bowness said. "I know we only scored one goal, (but) we had lots of opportunities tonight and Fleury was outstanding for them as Khudobin was for us. But that's Dallas Stars hockey."
The Stars limited the Golden Knights to 12 shots on goal and 20 shot attempts through two periods but were outshot 13-2 in the third.
"We're not really happy with how we played in the third period," Klingberg said. "I think we had a few chances to score 2-0 within the second period. [Khudobin] stepped up today and played a great game for us. He won the game for us. I think we gave them a little too much life in the third period, but we'll take it. We'll move on and we're up 1-0 (in the series)."
Video: Khudobin, Klingberg help Stars edge Golden Knights
Vegas was shut out for the second time in its past three games (4-0 loss to Vancouver in Game 6) and has scored four goals in its past four games, including two into an empty net.
"They were exactly what we expected them to be," DeBoer said. "They make you work for your offense, and if you're not willing to work for offense and support offensively, they're not going to hand it to you, and I think that was the case tonight."
The 25 shots on goal were the fewest this postseason for the Golden Knights, who had at least 33 in each of their prior nine games.
"Tonight it just took us too long to get into the game, took us too long to get that energy, that fire, that bravado that you need to play in these types of games," Golden Knights defenseman Nate Schmidt said. "You're in the final four. Every team is good here."
NOTES: Khudobin is the fourth goalie to get a playoff shutout for the Stars since they relocated as the Minnesota North Stars prior to the 1993-94 season, joining Ed Belfour (eight), Marty Turco (four) and Kari Lehtonen (two). … Johnny Bower (38 years, 142 days) is the oldest goalie to get his first playoff shutout, doing so for the Toronto Maple Leafs in a 2-0 win against the Montreal Canadiens in Game 3 of the NHL Semifinals on March 30, 1963.
NHL.com columnist Nicholas J. Cotsonika contributed to this report