Michal Neuvirth made 26 saves for the Flyers, who have lost four in a row.
The shutout was Saros’ second of the season and the sixth of his career.
Making his first start since Dec. 15, Saros was busy early, stopping 13 shots in the first period. He made 12 saves in the second and seven in the third period. His best sequence came just over three minutes into the second period when he made back-to-back saves in close on Sean Couturier and Jakub Voracek.
Saros also denied Wayne Simmonds on a breakaway just under six minutes into the third. That save came just before Arvidsson scored his second goal of the night on a wrist shot from the slot at 6:15.
Smith scored the game’s first goal at 2:03 of the second period.
Kevin Fiala skated the puck into the Philadelphia zone on the left side. From the left circle, Fiala sent a cross-ice pass to Smith at the right faceoff dot, where his wrist shot beat Neuvirth high to the stick side just underneath the crossbar.
Fiala has five points in his last three games.
Arvidsson made it 2-0 at 12:03 of the second.
In the left circle, Ryan Johansen drove toward the Philadelphia net before slipping a pass to Arvidsson, who was unchecked at the back post. He tapped it in for his second goal in as many games.
Arvidsson played his fourth game since missing 21 with a broken thumb.
Grimaldi scored his third of the season at 11:37 of the third.
NOTES: Nashville is 18-2-0 when scoring first this season. … the Predators are 12-3-1 against Eastern Conference opponents. … This was the 11th time the Predators played on New Year’s Day, all at home. … Philadelphia did not convert on either of its power plays in the game. The Flyers have not scored with the man-advantage in their last four games. … The Flyers are 1-16-3 when trailing after two periods.
Flyers: Host Carolina Hurricanes on Thursday.
Predators: Visit Detroit Red Wings on Friday.