Cam Lund scored his first NHL goal for the Sharks (20-43-9), who are 2-3-0 in their past five games. Alexandar Georgiev made 27 saves.
"I didn't like our start," Sharks coach Ryan Warsofsky said. "[We] weren't skating or physically engaged."
Panarin gave the Rangers a 1-0 lead at 12:04 of the first period. After Vaakanainen's stick broke on the one-timer attempt, the puck went to the right for Braden Schneider, whose cross-ice pass found Panarin alone in the left circle. His wrist shot beat Georgiev blocker side.
Panarin made it 2-0 at 13:58. He walked the blue line and fired a wrist shot through traffic that beat Georgiev blocker side.
Fox made it 3-0 at 4:48 of the second period. Mika Zibanejad stole the puck and fed on the right wing to Brennan Othmann, who sent a cross-ice pass to Fox for the shot into the open net.
"[Panarin] and Fox each had good games," Othmann said. "Two offensive players, and we rely on those guys a lot. It is good for them to step up."
Jonny Brodzinski made it 4-0 at 3:08 of the third period. Brodzinski walked down the left wing, and his wrist shot from the top of the circle deflected in off of Georgiev's glove.
Fox scored his second to make it 5-0 at 5:47. Miller's shot from the side of the net went off Georgiev and sat on the goal line for Fox to tap in.