Fleury, who has won five of his past six starts, made 31 saves for Vegas (7-4-0), which forced overtime when Nick Holden scored with 1:33 remaining in the third period. The Golden Knights finished 2-1-0 on a three-game road trip.
"Yeah, it's big, you know?" Fleury said. "The standings will be close until the end of the season. It's tough to make the playoffs, and all those points we get are important. I thought our game got better as the game went on, right? We played a solid third period and very happy to see Nick Holden] get that big goal for us."
***[WATCH: [All Golden Knights vs. Blackhawks highlights]*
Kirby Dach scored his first NHL goal, and Robin Lehner made 33 saves for Chicago (2-3-2).
Dach, the No. 3 pick of the 2019 NHL Draft, gave Chicago a 1-0 lead at 16:15 of the first period near the left side of the net on a redirection of Olli Maatta's shot from the edge of the right face-off circle.
"It was a pretty cool moment," Dach said. "[I] grew up dreaming of playing in the NHL, and two games in, you've got your first goal. That's pretty special, but at the same time, pretty disappointed that we lost. My main focus is the team game, so I've got to take a step back and realize what I can do better to help the team win and move forward tomorrow."