Sam Bennett scored two goals for the Panthers (30-9-5), who are 22-3-0 at home this season. Barkov had an assist, and Spencer Knight made 24 saves.
Florida tied the NHL record for the most victories through 25 home games, which had been done four times, most recently by the 2011-12 Detroit Red Wings (22-2-1).
"We have a lot of confidence at home," Panthers coach Andrew Brunette said. "I really believe we feed off the crowd. Tonight had an amazing feel. It felt a little bit like a playoff game there. We hope we can keep it going. It's a pretty good number. But we've still got a lot of hockey left."
Zach Whitecloud scored for the Golden Knights (25-16-3), who had their three-game point streak (2-0-1) end. Robin Lehner made 28 saves.
Vegas forward Max Pacioretty had two shots in 20:18 after missing 10 games with a wrist injury, and Golden Knights forward Reilly Smith had three hits in 16:21 after missing two games while in NHL COVID-19 protocol.
"I saw a lot of effort and a little bit of a lack of execution," Vegas coach Pete DeBoer said. "We were just off a little bit.
"We had a couple guys just coming back, so you expect some of that."
Barkov's shorthanded goal at 19:31 of the first period was his 500th point. He tied it 1-1 on a one-timer off a feed from Anton Lundell after stealing the puck from Smith in the neutral zone.
Bennett gave Florida a 2-1 lead at 1:18 of the second period with a wrist shot on an end-to-end rush. It was his 19th goal of the season, surpassing his previous NHL career high of 18, set in 77 games with the Calgary Flames in 2015-16.
"It's a cool milestone to hit," Bennett said. "I'm playing with confidence right now. I've been playing with great players all year and getting a lot of opportunities. I'm having a blast right now."
