Erik Haula had a goal and an assist for the Predators (27-21-2), who have won three of four.
"I've been just trying to take it game by game and not think about too much ahead," Saros said. "Just trying to focus one period at a time and give the team a chance to win. Even today when Florida had their time, as a team I think we really stuck together. You always kind of feed off of your teammates too when you see guys blocking shots and giving their all and stuff like that. It's always fun to see that."
The Predators are in fourth place in the eight-team Discover Central Division, two points ahead of the Dallas Stars, who have two games in hand. The top four teams will qualify for the Stanley Cup Playoffs.
The Panthers are second in the Central, two points behind the Hurricanes and one point ahead of the Tampa Bay Lightning. Florida could have clinched a playoff berth with a win.
Sam Bennett scored for the Panthers (31-14-5), who are 4-2-0 in their past six games.
"We wanted to throw some pucks at [Saros] and get some rebounds and wanted to be better in the blue paint today," Florida defenseman Radko Gudas said. "I thought we did a pretty good job of getting pucks through. We just couldn't get the rebounds that we wanted. We couldn't get the shots through when we got good screens. We were most of the time on the wrong side of the rebounds."
The teams will play again here Tuesday.
Bennett gave the Panthers a 1-0 lead at 4:49 of the first period when Anthony Duclair's pass went in off his skates. Bennett has scored seven points (four goals, three assists) in six games since being traded to the Panthers from the Calgary Flames on April 12.