Roman Josi had two assists to extend his point streak to a career-high nine games, tying Shea Weber for the longest streak in franchise history by a defensaeman. Ryan Johansen and Yakov Trenin also scored, and Pekka Rinne made 23 saves.
Alex Iafallo scored on the power play and Jack Campbell made 34 saves for the Kings, who have lost five of their last seven games.
Grimaldi made it 1-0 at 10:21 of the first period by scoring off his own rebound, with Josi getting the secondary assist.
Johansen extended the lead to 2-0 with 14 seconds remaining by burying a one-timer off Josi’s pass.
Josi has seven goals and 10 assists during his point streak, including nine assists in his past five games.. Weber had a point in nine straight games Dec. 31, 2010-Jan. 16, 2011.
Iafallo cut the deficit to 2-1 at 5:57 of the second period with a wrist shot from the slot after Tyler Toffoli stole the puck from Josi in the offensive zone. Iafallo has two goals and five assists during a six-game point streak.
Trenin put the Predators back up 3-1 at 9:37 of the third, tipping Matt Irwin’s shot from the point to send the puck bouncing in.
Smith made it 4-1 at 10:46.
NOTES: Predators F Matt Duchene was a late scratch because of illness. … Predators D Dante Fabbro (upper body) is day-to-day. … Kings D Joakim Ryan (lower body) was placed on injured reserve Saturday.
Predators: At Anaheim on Sunday.
Kings: Host Columbus on Monday.