Fleury made 28 saves, including 11 without allowing a goal in the third period, when Vegas scored three times.
"They already had a couple of goals on the power play and took the lead in the game, and from that point I thought our guys battled real hard and played really well in front of me and we kept the puck out," Fleury said. "The third period they played awesome."
He had last played Aug. 15, a 2-1 win against the Chicago Blackhawks in Game 3 of the first round, the first of back-to-back games. He made 26 saves, allowing a third-period goal to Olli Maatta.
"I felt those two weeks early in the game," Fleury said. "I think I was jittery, moving a little too much, but by the second (period) had a few more shots and started feeling better and by the third I thought I was back to normal, and my teammates really did a good job in the third, so they made my job easier too."
Robin Lehner started the other nine postseason games for Vegas, including the first three against Vancouver. He shut out the Canucks 5-0 in Game 1 on Aug. 23 and 3-0 in Game 3 on Saturday to give the Golden Knights the lead in the best-of-7 series.
Vegas can advance to the Western Conference Final by winning Game 5 on Tuesday. Teams with a 3-1 lead are 284-29 winning a best-of-7 Stanley Cup Playoff series, including a 6-0 in the first round this season.
Lehner is 7-2-0 with a 2.08 goals-against average, .921 save percentage and two shutouts in the postseason. Fleury is 3-0-0 with a 2.67 GAA and .893 save percentage.
Fleury started each of the Golden Knights' first 27 Stanley Cup Playoff games after they entered the NHL in 2017-18 and helped them reach the Stanley Cup Final in 2018, which they lost to the Washington Capitals.
"He's such an important part of our group and the effort our guys gave in a back-to-back situation, third game in four nights, in the third period, showed what they think of him," Vegas coach Peter DeBoer said.