Smith's first overtime goal in the Stanley Cup Playoffs, off a deflection in the slot, extended the top-seeded Golden Knights' lead against the No. 8 Blackhawks in the best-of-7 series.
"It started the shift before that (with Nick Cousins, Nicolas Roy, Alex Tuch)," Smith said. "All five guys did a good job cycling the puck, creating opportunities, and kind of hemmed them into their zone. Cousins did a great job of creating time and [my linemate Paul Stastny] made a great pass. I was fortunate enough it took a great bounce off my stick."
[WATCH: All Blackhawks vs. Golden Knights highlights]
Teams with a 2-0 lead are 324-51 (86.4 percent) winning a best-of-7 NHL playoff series.
Game 3 is in Edmonton, the Western hub city, on Saturday (8 p.m. ET; NBC, CBC, SN).
Stastny, Tomas Nosek and Mark Stone scored, Jonathan Marchessault had two assists, and Robin Lehner made 22 saves for the Golden Knights. Vegas was without forward Max Pacioretty (unfit to play), who was their leading scorer with 66 points (32 goals, 34 assists) in the regular season.
"[Smith's] been real impressive," Golden Knights coach Peter DeBoer said. "He was great before the [pause], but I think he's come back from the pause with a lot of confidence, a lot of energy. He's really driving a lot of plays and important plays. He has that ability to get hot.
"He's done it before and he's in one of those places right now, so we'll keep that going as long as we can."
Video: CHI@VGK, Gm2: Stone taps home rebound in front
Kirby Dach, Dominik Kubalik and Dylan Strome scored, and Patrick Kane had three assists for the Blackhawks. Corey Crawford made 35 saves, including 16 in the third period.
Kane passed Bobby Hull (129 points) for third in Blackhawks history in playoff points with 130 (Stan Mikita, 150; Denis Savard, 145).
"I thought we were playing really well the first two periods, and for whatever reason it just seemed that they came out better than us in the third," Kane said. "I don't know if we thought it was going to be a little bit easier than it was, especially after we tied it up (3-3). They're a good team, they're going to fight back, and they carried the play for most of the third, so we didn't generate much."
The Golden Knights have outscored the opposition 11-1 in the third period and overtime in their five postseason games, including three wins in the round-robin portion of the Stanley Cup Qualifiers.
"When we're playing our game, we can win different ways," Stastny said. "When [DeBoer] came in (as coach Jan. 15), he brought a new sense of life into us and I think we changed a few things. All of sudden, we're spending less time in the defense zone and playing more as a team. We found different ways to win with different guys. We play a good team game and there aren't a lot of teams that can play our style for 60 minutes ... it's all about playing the way we want to play."
Video: CHI@VGK, Gm2: Dach shovels home rebound in front
Stastny gave the Golden Knights a 1-0 lead when he scored from the slot at 10:44 of the first period.
Nosek made it 2-0 on a shot from the right face-off circle at 15:35.
Nosek, who replaced Pacioretty in the lineup, did not return for the third period after playing 9:23 in the first and second. As part of the NHL Return to Play Plan, a team is not permitted to disclose player injury or illness information.
DeBoer had no update on Pacioretty or Nosek after the game.
Dach scored his first NHL postseason goal on a backhand at the right post at 3:17 of the second period to pull the Blackhawks within 2-1.
"[Vegas] comes at you in waves, and we did a good job of weathering the storm," Dach said. "We have to get more pucks toward the net, get our shots through. They're good at collapsing down low. Once we find our groove, we'll be OK as a group. We had chances in overtime to put the game away, but it didn't happen that way."
Video: EA Sports OT Winner: Smith first career OT goal
Kubalik tied it 2-2 with a power-play goal on a wrist shot from the high slot at 12:07 of the second period.
Stone shot a loose puck into the net that deflected off his chest at the left post at 17:20 to give Vegas a 3-2 lead.
Strome tied it 3-3 with 14 seconds remaining in the second on a shot at the left post off a backhand saucer pass from the bottom of the right circle from Kane.
Lehner hasn't lost since being acquired by the Golden Knights on Feb. 24 in a trade from the Toronto Maple Leafs, who earler that day acquired him from the Blackhawks; he is 4-0 in the postseason after going 3-0-0 in regular season.
"It's a very tight-knit group and everyone buys into the system and does the right things," Lehner said. "I think in the long run, you get rewarded. From a goalie's perspective, letting in a goal, there's no panic. You trust the team can come back. It's a well-structured team and a lot of skill at the same time so we need to keep it going."
NHL.com staff writer Tracey Myers contributed to this report
Video: Smith's OT winner leads Golden Knights by Blackhawks