"I thought we had a really good game," said Lehner, whose shutout was his second of the series; he made 26 saves in a 5-0 win in Game 1 on Aug. 23. "They had a really good first, but in the second and third periods, the guys really helped me out. It's a fun team to play against ... they're easy to get up for."
Alex Tuch, Zach Whitecloud and Mark Stone scored for the Golden Knights, the No. 1 seed in the West who are 7-0-0 when scoring first this postseason.
Jacob Markstrom made 31 saves for the Canucks, the No. 5 seed.
"I liked our start to the game, and we were unlucky to be down 2-0," Canucks coach Travis Green said. "That happens in playoff hockey. With our team, sometimes when we get down, we tend to overpass the puck a little bit. We had a few too many east-west plays in the offensive zone, especially in the second period.
"I really liked our first period. ... We skated well, drew some penalties. Give [Lehner] credit. He made some really nice saves. I think we could've easily been up after the first period."
[WATCH: All Golden Knights vs. Canucks Game 3 highlights]
Teams that win Game 3 after a Stanley Cup Playoff series is tied 1-1 are 218-107 (67.1 percent) winning a best-of-7 series, including 3-1 in the first round.
Game 4 will be in Edmonton, the West hub city, on Sunday (10:30 p.m. ET; NBCSN, CBC, SN, TVAS).
Tuch gave Vegas a 1-0 lead at 4:05 of the first period, skating in on a breakaway after receiving a lofted pass from Nicolas Roy and scoring glove side from the left circle. Tuch, who scored eight goals in 42 regular-season games, has seven in 11 postseason games.
"I'm not trying to think about the regular season and focus on the playoffs," Tuch said. "We had a break to get healthy and I tried to get in the best shape possible. I think I was able to do so with the help of our coaching staff and my teammates."
Tuch has scored in four straight postseason games to tie Jonathan Marchessault (2019) for the longest streak in Vegas history.
"Alex is a guy we knew we were going to need (in the postseason)," Golden Knights coach Peter DeBoer said. "He was disappointed with his regular season, and we talked about the fact if you have a great playoff, no one will remember the regular season, and he's taken that and run with it.
"He's been fantastic, and not just sticking the puck in the net, but his speed is dangerous every time he's on the ice."
Video: Lehner, Vegas blank Canucks, take 2-1 series lead
Whitecloud made it 2-0 at 5:28 of the first following a turnover by Quinn Hughes in the Canucks zone. Whitecloud took a drop pass from Max Pacioretty and scored on a wrist shot past Markstrom, who was screened by Vancouver defenseman Christopher Tanev.
Lehner made 16 saves in the first period, with nine against three Vancouver power plays, including three during a 5-on-3. He is 4-4-0 in nine games against the Canucks (regular season and Stanley Cup Playoffs), with each of his four wins a shutout.
"[The 5-on-3] is a huge momentum opportunity for them or for us if we kill it, and I think we dug in, got some big saves from Robin," DeBoer said. "He was our best player in the first 10 minutes and allowed us to get through some of that. Your special teams, a lot of times, are a direct reflection on what your 5-on-5 game looks like, and I thought our 5-on-5 game was in a good place tonight."
Stone extended the lead to 3-0 on a power play with a snap shot from the right face-off circle at 2:19 of the third period.
Vancouver was 0-for-5 with the man-advantage; Vegas was 1-for-4.
"On the 5-on-3, we had about as many good looks and executed about as well as we could," Canucks forward J.T. Miller said. "The goalie made some nice saves, got momentum for the team. We easily could've tied the game or got back close."
Video: Lehner earns Saturday's Pepsi Zero Sugar Shutout
The game was rescheduled from Thursday after the players on the eight remaining teams decided not to play as a form of protest against systemic racism and police brutality.
"There are certain things bigger than hockey," Golden Knights defenseman Alec Martinez said. "I'm proud with the way the guys responded. Not just our team, but the League as a whole. That said, it was a good time for thought and reflection and discussion.
"But now it's back to hockey and we're just focused on tomorrow night."
The Canucks did not say if Markstrom or backup Thatcher Demko would start Sunday, and the Golden Knights did not say if Lehner or Marc-Andre Fleury would be their starting goalie.
"I don't know, we'll see what coach says," Lehner said. "No matter what people think, it's a great thing to have. I mean, there's going to be some discussions, debates, and some people are not going to be happy all the time with who's playing, but at the end of the day, whoever plays, just go out and do their best. There's a very tight group in this locker room, and we're all supportive of each other, and whoever plays, everyone supports, so it's a good situation inside the locker room and hope everyone can just get behind that."
NHL.com staff writer Tracey Myers contributed to this report