Nashville has won five of six and has earned at least one point in seven straight games. Florida's three-game winning streak was snapped.
Lindback, a rookie goalie from Sweden who earned the start over injured No. 1 netminder Pekka Rinne, improved to 6-1-2.
"It's a great feeling," Lindback said of the shutout. "The guys are doing a really great job in front of me. I only take the first shot, and if there are any rebounds that get through, they get them out for me."
The 6-foot-6 Lindback has started four straight since Rinne injured a leg on Dec. 1 at Columbus. Lindback is 3-0-1 since taking over the workload.
"We got a good start and played very disciplined," Nashville coach Barry Trotz said. "He made a couple of really key saves for a goaltender who didn't have a lot of shots in the first half of the game."
Suter gave Nashville a 1-0 lead 1:14 in when he connected on a one-timer from the left circle off a pass from Martin Erat. Sergei Kostitsyn also assisted on Suter's goal, extending his point streak to a season-high five games.
"I think it is just a matter of taking what they give you," Suter said. "Obviously you want to contribute every night, and tonight I was fortunate enough to be able to."
Weber doubled the Predators lead at 16:49 of the first period.
Suter carried the puck behind the Florida net and found his defense partner at the top of the right circle. Weber scored with a one-timer over the glove of goalie Tomas Vokoun.
"I saw Sutes coming around the net," Weber said. "He made a good pass, and we had good traffic in front."
Vokoun spent eight seasons with the Predators before being traded to the Panthers in June 2007. He holds the Nashville franchise record for wins, shutouts, and games played by a goalie.
Coming off of a shutout win in Washington on Thursday, the Panthers couldn't recover from their poor start.
"Obviously, the first period was the game." Florida coach Peter DeBoer said. "They came out with a couple of big hits and a couple of big goals. They won the first period, and from then on, that's a hard team to come from behind against."
Florida's last win in Nashville was Dec. 11, 1999.
"We weren't ready for their pressure," Panthers center Stephen Weiss said. "We were just smacking pucks around and running around in our own zone, and we consequently gave up two goals."
Ward made it 3-0 with an empty-net, power-play goal in the final minute.
This was Suter's first two-point game this season. ... The Predators are 5-1-4 against the Eastern Conference this season and 4-0-2 against the Southeast Division. ... Florida will play only one of their remaining 54 games outside of the Eastern time zone -- March 23 at Chicago. Florida D Bryan Allen missed a ninth game because of a foot injury.