Adin Hill made 38 saves, and Kolesar had two assists for Vegas (28-13-2), which has won four of its past five games.
"It was a competitive game. It was intense. It was physical," Golden Knights forward Jack Eichel said. "Both teams brough it tonight. Credit to our group, we stuck with it. We were down a goal in the third period. We found a way to get a long 5-on-3 penalty kill. Then we found a way to win a hockey game in regulation. So, I give everyone credit in this room. Everyone stepped up tonight."
Vegas forward Mark Stone left the game midway through the first period with an upper-body injury. Stone, who is Golden Knights captain, has 38 points (17 goals, 21 assists) in 43 games this season.
"I can't give you that right now because I don't know [the status of his injury]," Vegas coach Bruce Cassidy said. " … He's obviously a big part of our team. He's the captain. He has an injury history. So, I know there's going to be questions. I just don't have the answer right now. Hopefully I can give you something more positive tomorrow."
Nick Cousins and Sam Reinhart scored, and Bobrovsky made 29 saves for Florida (19-20-4), which is 0-4-1 all-time at Vegas.
"After the first 10 minutes of that game, we were good straight through. That's it," Panthers coach Paul Maurice said. "We had the 5-on-3 and don't score, that will be the turning point. We got to finish. When you're on the road, you've got to finish on your 5-on-3s when you get a chance. You've got to finish on your chances."
The Golden Knights killed off the 5-of-3 penalty at 3:25 of the third period. In the second half of the third, they scored three consecutive goals on six shots.
"A 5-on-3 kill can turn momentum around in a second," Hill said. "Just like it did [tonight]. After that, we kind of got going. It was a great job by [Alec] Martinez and [Brayden] McNabb there to block some shots and make a couple clears for us."
The Panthers took a 1-0 lead when Cousins was awarded a goal at 2:02 of the first period after a scramble in front that knocked the net off its moorings. Following a review initiated by the NHL Situation Room, officials ruled the net came loose due to Golden Knights defenseman Ben Hutton knocking Florida forward Eric Staal into it and awarded Cousins the goal.