Winnipeg outshot Vegas 16-8 in the third period and 32-20 after the first.
But Fleury finished with 33 saves, and the Golden Knights won 4-2 to take a 2-1 lead in the best-of-7 series with Game 4 here on Friday (8 p.m. ET; NBCSN, CBC, SN1, TVAS).
It was just another day at the office for Fleury.
"I was having a little fun," he said. "They were good chances and I was happy to get, especially that second one. The emotion, I was having a little fun in there."
Golden Knights coach Gerard Gallant said, "He's made unbelievable saves. They were obviously important at a key time for us. That's Fleury. He's been great all playoffs, he's been great all year for us. He's a guy that has fun out there. I'm sweating on the bench yelling my head off and I look down there and he's just having fun."
After allowing four goals in Game 1 (a 4-2 loss), Fleury has allowed three goals (.955 save percentage) in the past two games against a Winnipeg team that has scored 3.33 goals per game in the playoffs.
"Unbelievable," Vegas forward Alex Tuch said. "He had how many, 30-something saves this game? He had a lot of unbelievable saves. [Winnipeg] had a lot of good looks."
The Golden Knights are two wins away from reaching the Stanley Cup Final, and the main reason is, arguably, their goaltender. Fleury, who is going for his third straight Stanley Cup and fourth overall, has four shutouts and leads all remaining goaltenders in save percentage (.945) and goals-against average (1.70).
"I don't think anybody saw us here," Fleury said. "It's been a long season. It's been a lot of fun to be part of it. Really proud to be proud of this team and the way these guys have been working. We deserve to be here."