Guentzel curled a shot around the right post to give Pittsburgh a 5-4 lead. It was upheld after review, and Rust scored an empty-net goal to make it 6-4 with 38 seconds left.
"The emotions of the game were so high and low," Guentzel said. "I think you're going to go through that during the stretch of the season. So just to come out on top, I think it's big for us. We're finding different ways to win."
Pittsburgh goalie Matt Murray made 44 saves for his first home win, second overall, since Nov. 9.
The Predators, who trailed 3-0 in the first period, tied the game after falling behind 4-1 late in the second.
"We all knew that was bad in the first," Josi said. "We need to show a response, especially after last night and losing that game at home. We need to come out strong, and we were mad about our first period. So it was a good response, but we have to do it for 60 (minutes)."
Craig Smith made it 4-2 at 16:03 of the second period before Granlund scored twice. He cut it to 4-3 on a wrist shot with Murray scrambling in front of the crease with 59 seconds remaining in the second, and batted the puck out of the air to tie it 4-4 at 8:56 of the third period.
"Not a good start, obviously. It wasn't good enough at all," said Granlund, who has six goals this season. "Second period, we started playing the way we can play, play with the puck and not just throwing it away. Winning some battles. We found a way to get back in the game, but that's obviously a tough ending there."