Sceviour gave Florida a 1-0 lead one minute into the second period with his fourth goal. He won a battle for the puck along the end boards and skated behind the net. Jones stopped his wraparound, but Sceviour pounded the rebound inside the left post.
After a turnover by Sharks defenseman Tim Heed, Bjustad took a pass from former San Jose forward Jamie McGinn and beat Jones from close range at 12:33 of the third period to make it 2-0.
Luongo made 17 saves in the third period.
"I thought the first 40 minutes was probably some of the best hockey we've played all year as far as systems wise," said Luongo, who had never shut out the Sharks. "It's not easy to come in this building. We know they like to come out hard.
"I think we did a great job in the first and in the second period as well; they didn't have much. Obviously, they're going to have a push in the third to try to tie it up, but we were able to hold the fort there, so that was nice."
Heed scored with a slap shot at 4:37 of the second period, but the goal was disallowed after Boughner challenged and video review showed the puck left the Panthers zone before Heed made contact.
"Right when Heed shot that puck, we all looked at each other and we said, 'That's got a chance to be offsides,'" Boughner said. "Then we looked down at the TVs. But ultimately, we got to rely on [Ben Cooper], our video guy, and [goaltending coach Robb Tallas] upstairs. They were all pretty confident there."