Bobrovsky was starting for the second consecutive day after making 33 saves in a 4-1 win against the Columbus Blue Jackets on Saturday.
"I felt great there," Bobrovsky said. "It was great to come back tonight and compete with my teammates. Physically, you feel a little bit fatigued there, but I thought we stood together at the right time. It's a huge two points for us."
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Aleksander Barkov, Keith Yandle and Frank Vatrano each had a goal and an assist, and Jonathan Huberdeau had two assists for Florida (15-9-5), which went 2-for-4 on the power play and has won three of its past four games.
Kevin Labanc scored, and Martin Jones made 28 saves for San Jose (15-15-2), which is 0-3-1 in its past four games, including a 7-1 loss to the Tampa Bay Lightning on Saturday.
"My disappointment tonight is a little like last night," Sharks coach Peter DeBoer said. "I think they score on their first shot or their first couple shots. You're chasing the game right off the bat. It's tough on the road to do that. I thought we hung in there and kept fighting, but it wasn't enough."
Yandle put the Panthers ahead 1-0 on the power play at 4:31 of the first when he shot between the legs of Sharks forward Melker Karlsson from the left point.