Rinne earned his NHL-leading 34th win of the season; he is 15-1-1 in his past 17 games. He was credited with five saves during a three-second span on a San Jose power play in the second period.
"Pekka is unreal," Smith said. "He stays with it. I think the whistle blew, and he stayed with it even after [Sharks forward Joe Pavelski] shot it. That's nothing new to anybody else here. He's a competitor, and he wants to win on every shot."
Nashville (39-12-6) is 25-3-1 and has won 14 of the past 15 games at home. The Predators have won six straight games overall.
San Jose (29-22-8) is 2-5-2 in February and 1-4-1 in its past six games.
"[Rinne] was very tough to beat, obviously," Sharks coach Todd McLellan said. "He stood his ground and played a tremendous game. The number of saves he made on the power play where we had a chance maybe to crawl back into the game, he did an exceptional job."
Defenseman Matt Irwin gave San Jose a 1-0 lead at of the first period on his fifth goal of the season. Irwin was sprung by a pass from forward Melker Karlsson for a breakaway, and he beat Rinne on stick-side.
"Offensively, we created a number of chances, maybe more than we have in a long time against a pretty good defensive team," McLellan said. "That's a positive, but they didn't go in. We've still got to clean up a lot of things defensively."
Nashville defenseman Shea Weber tied the game 1-1 at 13:42 of the first period on a slap shot from the point. Weber took the puck off of a faceoff win by Mike Fisher and took a shot that beat San Jose goaltender Alex Stalock for his 14th goal of the season.
Smith gave Nashville a 2-1 lead at 16:02 of the first period on a rebound of a shot taken by defenseman Mattias Ekholm. Smith batted the puck out of mid-air past Stalock for his 16th goal of the season. Mike Ribeiro made a turnaround pass through three defenders to keep the puck in the offensive zone.
"It was great," Smith said. "It's a testament to [Ribeiro's] ability. I think he had three or four guys around him, and he was still calm as a cucumber. He's able to make plays and find guys."
Smith scored another goal 52 seconds into the second period on the power play. There was a scrum in front of Stalock and Smith was able to tap the puck past him for his 17th goal of the season.
"It felt tight the whole game for some reason," Smith said. "They put a lot of shots up and at times they held some pretty good pressure. We have a good goaltender that can help us with great saves that keep us moving forward. All in all, I think it was a great game."
"We had a good balance tonight, I thought, and contributions from the lines," Predators coach Peter Laviolette said. "I thought the second period, we really got going more with our game and [were] able to come out and play a little bit more aggressive. You see some goals as a result from that."
James Neal made it 5-1 at 10:31 of the second on a wrist shot while on a rush. Neal took a pass from Ribeiro and beat Stalock through the five-hole for his team-leading 20th goal of the season, marking the seventh time in his career that he's scored 20 goals.
Defenseman Anthony Bitetto was recalled by Nashville from the Milwaukee Admirals of the American Hockey League on Tuesday, but his equipment did not arrive in time for the start of the game. Nashville had to start with five defensemen until Bitetto arrived on the bench at 6:26 of the first period. Anton Volchenkov was placed on injured reserve.
"Actually it's good, because you’re playing every second shift so you get into the game right away," Weber said. "Obviously [Bitetto] comes back, I think it's more of a challenge for him trying to get into the game with no warm-up, no skate or nothing. He did a really good job though. Given the circumstances, he played really well for us."
Nashville hopes to have defenseman Cody Franson and forward Mike Santorelli for the game at the New York Islanders on Thursday. The Predators acquired Franson and Santorelli from the Toronto Maple Leafs on Sunday.