Bobrovsky got his second shutout of the season and the 51st of his career.
Sam Reinhart scored his ninth goal in the past 12 games for the Panthers (11-8-1), who have won four of five.
Jake Allen made 23 saves for the Devils (13-6-1), who have lost two in a row. New Jersey was shut out for the first time this season.
Reinhart made it 1-0 12:58 into the first period by scoring on the rush. He drove around Devils defenseman Luke Hughes in the left face-off circle and put a wrist shot off the right shoulder of Allen.
Reinhart has nine points (four goals, five assists) during a five-game point streak and 14 points (nine goals, five assists) in his past 12.