David Legwand netted the winner late in regulation, as Nashville claimed a 3-1 victory over Colorado at Bridgestone Arena.
Patric Hornqvist also tallied and Taylor Beck added two assists for the Predators, who put the brakes on a three-game slide and avenged a 1-0 overtime loss in Denver last Saturday.
"It's really important because we're right in the thick of things right now," Nashville head coach Barry Trotz said.
Pekka Rinne stopped 25 shots.
Matt Duchene posted the lone score for the Avalanche, losers in nine of their last 11.
Jean-Sebastien Giguere made 35 saves in defeat.
"Giguere played one heck of a game for us, and that was definitely not the way to repay him," Duchene said.
Legwand took control of a loose puck behind the net to the right of Giguere, curled in front and slipped the disc home through the veteran's five-hole with 1:14 on the clock.
Gaustad slid the insurance marker into the empty net with 15 seconds left.
Giguere and Rinne matched each other save for save through the first 40 minutes, as the former made 20 stops and the latter turned away 16.
Duchene snapped a scoreless deadlock with 61 seconds played in the third period, outracing three Predators pursuers from inside his own zone and beating Rinne low and through the pads.
Nashville tied the game at 8:23, when a Beck shot was slowed but the loose puck ticked off Hornqvist's skate in the crease and over the goal line. A review determined there was no kicking motion.
Rinne won for the first time in his last four starts ... Beck posted his second career multi-point effort and his first career two-assist game ... Nashville hosts Columbus on Thursday and Colorado hosts Detroit on Friday.