Trailing 2-1, Jiri Hudler got the rally started with the tying goal 2:36 into the third period. It came on a set-up from rookies Markus Granlund and Gaudreau.
After TJ Brodie's pass deflected in off Predators defenceman Shea Weber to give the Flames the lead at 4:23, Calgary went ahead by two goals two minutes after that.
Gaudreau darted down the left wing and after the 5-foot-9 rookie showed good strength in fending off the stick check of Craig Smith, he then whipped a shot from a bad angle that beat Pekka Rinne over his shoulder.
After beginning the season with no points in his first give games, a stretch that culminated in him being a healthy scratch, Gaudreau has two goals and four assists in his last six games.
Sean Monahan also scored for Calgary (6-4-2). The Flames finish 2-1-2 on a five-game homestand. They begin a five-game road trip Sunday night in Montreal.
James Neal paced the offence for Nashville (6-2-2) with two goals — his sixth and seventh of the season. Craig Smith also scored. The Predators have split the opening two games of a season-long six-game road trip, which continues Sunday in Vancouver.
The banged up Flames were without three of their top centres for the season in Mikael Backlund (abdominal strain), Matt Stajan (knee) and Joe Colborne (upper body). They joined Mason Raymond (shoulder), who is also sidelined.
Tied 1-1 in the second period, Neal gave Nashville its first lead of the night at 11:09. Mike Ribeiro beat Monahan on a face-off, pulling the puck back to Neal at the top of the face-off circle. His quick shot through several sets of legs beat Jonas Hiller, who didn't appear to see it.
Neal and Ribeiro, who leads the team in points, were both acquired in the summer by Predators general manager David Poile in an attempt to generate more offence for his team, which finished 19th in scoring a year ago while missing the playoffs by three points.
Scoreless after 20 minutes, Monahan opened the scoring at 4:23 of the second by banging in a Dennis Wideman rebound for his third of the season.
The lead lasted only 67 seconds before Smith corralled a loose puck in front of the Calgary net and beat Hiller.
Hiller, who finished the night with 28 saves, improves to 3-2-1 on the season. The veteran goalie was making his second straight start for Calgary, which was significant in the fact that until tonight, coach Bob Hartley had been rotating Hiller and Karri Ramo.
In giving up a season-high four goals on 30 shots, Rinne sees his record fall to 6-2-1.
Notes: Brodie's four goals matches his career-high... Prior to the game, a moment of silence was held for ex-Stampeder and prominent businessman John Forzani. The 67-year-old Calgary native passed away from a heart attack... The game marked the NHL debut of Flames LW Michael Ferland and the season debut for C Markus Granlund... Ferland (upper body) left the game late in the second period and did not return after being shaken up after a hit by Anton Volchenkov... Back in the Flames line-up for the first time in a while were RW Devin Setoguchi and RW Brian McGrattan. They had been healthy scratches for the last four and five games respectively.