The shutout was the second for Drieger in the NHL, each against Nashville. The 26-year-old made 27 saves in a 3-0 win against the Predators in his first NHL start, Nov. 30, 2019.
Driedger made his first start since March 7 with Sergei Bobrovsky making the past five.
"We played a really, really good game throughout 60 minutes, great kills, great movement on the power play," Driedger said. "Hats off to Saros. He played a heck of a game himself. [I'm] feeling pretty good. That's a great win.
"Those games when the other goalie is putting on a show can get a little dicey. You kind of have to make sure that you're sharp. One mistake and that maybe can send it to overtime. [I] saw the pucks that came my way and it ended up working out."
Florida didn't score in the first period despite taking 22 shots and getting three power plays, including a four-minute man-advantage when Mathieu Olivier was assessed a double minor for roughing.
"It was one of those games where we looked like we're throwing everything but the kitchen sink and when we get nothing for it, but sticking with it was the best part about it from our end," Panthers coach Joel Quenneville said. "Whether it was a save or unable to score, I don't think we deviated how we were going about our game."
Barkov gave Florida a 1-0 lead at 9:15 of the second period when he took a centering pass from Anthony Duclair and lifted a backhand high into the net. It was Barkov's fifth goal in five games.
MacKenzie Weegar extended his point streak to seven games (one goal, eight assists) with an assist, tying Keith Yandle's Panthers record for defensemen set in 2018-19.