Smith's power-play goal, the Predators' second of the night, at 16:25 of the second period gave them a 3-1 lead. His goal early in the third period, his sixth of the season, made it 4-1.
"We wanted to make sure every shot counts, make sure the right play is going to be made," Smith said. "We tracked the defensemen hard tonight and we created some turnovers on the wall which we were able to convert into some offensive chances."
The Maple Leafs scored first when Peter Holland skated into the offensive zone and fired a wrist shot past goalie Marek Mazanec at 5:48 of the first period. It was Holland's second goal of the season, his first for the Maple Leafs after arriving in a trade from the Anaheim Ducks on Saturday.
Holland had room to gain when Predators captain Shea Weber laid a big hit on Nikolai Kulemin in the neutral zone. With Holland only having Roman Josi defending him, he let his shot go from the faceoff dot and past Mazanec.
"Obviously it feels good to get your first one as a Leaf," Holland said. "[Morgan] Rielly made a great play to head-man the puck, and [Kulemin] made a great play on the wall. I came in, I was originally looking pass and kind of saw that far side open up so I tried to put it on net and it went in for me. But obviously it would feel a lot better if we had two points tonight."
After Maple Leafs forward Mason Raymond picked up a high-sticking double-minor 1:25 into the second period, the Predators tied the game when Seth Jones scored his third of the season at 2:01. Jones' shot was deflected by a Maple Leafs player on the way to net and the redirection helped get the puck past goalie Jonathan Bernier.
"He's been great for us this year," Weber said of Jones. "Obviously a little bit of fortune on that one getting it through and hitting a stick, but sometimes you need those bounces and sometimes they go against you. It was a big goal for us, and our power play did a great job for us tonight."
The goal was the first the Predators scored on Bernier this season after he shut them out Oct. 10 in a 4-0 win in Nashville. Bernier stopped 24 shots and lost for the second time in 10 career starts against the Predators (8-2-0).
"He's owned us in the last couple years here when he was [with the Los Angeles Kings] and obviously the last game back," Predators coach Barry Trotz said. "It was good to finally get that. He was starting to get in our heads, so hopefully it'll be good for another year at least."
The Predators took a 2-1 lead at 11:14 of the second period when Cullen scored his fourth goal of the season. He received a quick pass from the half-boards from Gabriel Bourque and snapped a wrist shot by Bernier through his five-hole. Cullen assisted on the other three Predators goals.
A boarding call to James van Riemsdyk led to Smith's power-play goal in the second. Nashville went 2-for-4 with the man-advantage.
"I thought their power play was pretty good tonight," Bernier said. "They obviously scored some big goals on it."
The Maple Leafs cut the lead to 4-2 when Nazem Kadri scored his sixth goal of the season. He was playing his first game after a three-game suspension for hitting Minnesota Wild goalie Niklas Backstrom.
"We just didn't play well enough," Maple Leafs captain Dion Phaneuf said. "I don't think you can say much more than that. We didn't do enough of the little things against a team that always comes hard. They play very disciplined to their system, they have for a long time, and we just weren't good enough."
The Maple Leafs had limited chances after the first period; they put up 15 shots in the second and third periods combined after having 11 in the first. Mazanec made 24 saves.
"It was a group effort tonight, a whole team effort," Jones said. "It started back there with [Mazanec], he made big saves for us and it kind of worked its way up. I thought everyone played a great game tonight."
The win was the third in a row for the Predators.
"We had a tough stint there coming off a long road trip," Smith said. "We wanted to turn the ship around a little bit and I think we stayed on a few things we've been doing since the beginning of the year. If we stay the path, good things are going to happen."
The Predators return home to play the New York Rangers on Saturday. The Maple Leafs will host the Washington Capitals.