Smith has scored five goals in his past three games after a nine-game drought.
"It took me over 600 games to get a hat trick," Smith said. "It's obviously a big moment for me and I'm happy about it, but there's a lot of guys who helped me put the puck in the back of the net."
Chandler Stephenson scored, and Alex Pietrangelo had two assists for Vegas (39-12-3), which swept the back-to-back set here and finished 6-1-1 against St. Louis this season. The Golden Knights won 4-3 in overtime Friday.
Marc-Andre Fleury made 20 saves for his eighth consecutive win.
"As a group on the back end, I thought we got back a lot quicker," Pietrangelo said. "They have really good structure, so you've got to try and get that as quickly as possible. I thought we made good decisions with the puck tonight."
Colton Parayko scored, and Ville Husso made 26 saves for St. Louis (24-20-9), which had its eight-game point streak end (5-0-3). The Blues will finish fourth in the West.
"I didn't think we were very good for two periods," St. Louis coach Craig Berube said. "We know how to generate offense against them. Tonight, we weren't engaged early enough. We couldn't hit the net."