Nashville outshot Montreal 55-20 and the Predators have won two straight and six of their past eight. Montreal has dropped four of six. The 55 shots are a franchise record for Nashville.
Rinne got his second shutout of the season and ninth of his career. Sullivan had just two goals in the team's first 17 games of the season. Price made a career-high 53 saves for Montreal. The 53 saves tied Wayne Thomas' Canadiens record for most saves in a game. Thomas did it March 10, 1974 in a 5-4 win at Pittsburgh.
"They threw a lot of pucks at the net tonight," Price said. "Records aside, we were here to get two points, not a record."
"He performed well, there is no doubt," Canadiens coach Jacques Martin said of his goaltender. "It's unfortunate that his teammates didn't take advantage of a performance like that."
Sullivan scored his first goal at 10:48 of the opening period when he collected a rebound of his own shot and was able to beat Price with a backhand.
The Predators set a franchise record with 24 shots on goal in the first period. The previous record for shots in a period was 23 set Feb. 28, 2004, against the New York Rangers.
"It's just the mindset, you break down teams' defense when you put it on net," Nashville coach Barry Trotz said. "They are scrambling for pucks, they are reaching, and we are being firm in their offensive zone."
J.P. Dumont was credited with the only assist on Sullivan's goal. Dumont leads the Predators in points this season with 12.
"I'm not going to lie, I really feel comfortable with J.P., and I find that he really settles the play down for us in the offensive end," Sullivan said. "He's so good at puck protection and nifty little passes that when you are open, you are getting the puck."
Sullivan made it 2-0 at 12:59 of the third period.
With the Predators on a 5-on-3 power play, Price stopped a slap shot from Nashville defenseman Shea Weber, but the rebound came right to Sullivan in the left circle where he fired a one-timer by Price on the stick side.
Rinne has won six of his last seven and improved his record on the season to 6-4-0.
"The guys on defense did a great job, I didn't have to face too many shots," Rinne said. "Obviously you have your good saves and your moments, but it was one of the easier games that we have had this year so far."
- The Canadiens made their first trip to Nashville since Feb. 22, 2007.
- Montreal right wing Brian Gionta missed his first game of the season with a lower-body injury.
- Saturday's game was the first of five consecutive home games for the Predators. They play seven of their remaining eight November games at home.