It was Fleury's 46th NHL shutout, tying him with Rinne for fourth among active goaltenders behind Jonathan Quick of the Los Angeles Kings (47), Henrik Lundqvist of the New York Rangers (63) and Roberto Luongo of the Florida Panthers (74).
Smith and Theodore scored 1:31 apart in the second period.
Smith gave the Golden Knights a 1-0 lead at 12:10 when he scored on the power play. The goal ended an 0-for-12 drought for Vegas with the man-advantage dating to Dec. 23.
Theodore made it 2-0 at 13:41 when his slap shot from the point beat Rinne, trickling in through the five-hole.
"The second period wasn't bad with the exception of those four minutes," Predators coach Peter Laviolette said. "Inside of those four minutes, we made too many mistakes and it cost us the game. They're a good team."
Jonathan Marchessault scored into an empty net with 2:23 remaining to make it 3-0. He has a three-game goal streak and extended his point streak to seven games (five goals, six assists).
Predators defenseman Ryan Ellis made his season debut after recovering from offseason knee surgery. He had two shots on goal, one hit and two blocked shots in 18:27.
"I think at times in the game, we played really well, and then other times not so much," Ellis said. "At the end of the day, we didn't win, and that means my game isn't good enough right now."