Matt Halischuk added a goal and an assist for Nashville, which improved to fourth in the West with 97 points as it closes in on its sixth playoff berth in the past seven seasons.
"That was still a big one for us," center Mike Fisher said. "We're trying to move up and get that 4 spot if we can. That being said, we were playing a team that's out of it, so find a way to get up. We got some good bounces early and really put the game out of hand."
Nashville jumped out to a 3-0 lead in the first period, and the Predators earned their 23rd home win, making them the only NHL team to win that many each of the past six seasons. Fisher has a power-play goal and Patric Hornqvist had three assists.
For Tootoo, it was a career-best night with three points. All he wanted to talk about was focusing on finishing strong.
"Mentally, we've got to be prepared to play 60 minutes and not look too far ahead of us," Tootoo said. "We've got to live in the moment shift by shift and make the best of it. ... We need points. We want to win out the season here and then obviously be as high as we can in the standings."
"We waited until a little too late to get our goofy things to happen for us and score some goals," Atlanta coach Craig Ramsay said. "I can't blame anybody. When they got a chance, it went in."
The Thrashers came in 2-3-0 in their past five games, eliminated from playoff contention after their 3-2 loss to Boston on Saturday. They tried to make a game of it early as they took as many shots as Nashville, but the Predators had much better luck getting past goalie Chris Mason.
Halischuk backhanded the puck into the net from the slot at 5:24 for his third goal. Tootoo got an assist on the score, then took advantage of Antropov's failure to clear the puck from the crease after Mason had stopped Martin Erat's shot. He skated up and flipped the puck over the line at 19:19.
Kostitsyn made it 3-0 with 0.8 seconds left on the clock when he wristed the puck into the open side of the net.
"We outshot them, outskated them and outplayed them," Antropov said. "Then in a matter of minutes they got two goals at the end. It killed it. Big time. I thought we battled back a little bit. You have to give them credit and especially their goalie [Pekka Rinne]. He stood on his head and got some really nice saves."
The Predators chased Mason when Tootoo scored again at 1:56 of the second, helped again by Atlanta. Halischuk passed the puck toward the slot and a Thrashers player apparently tipped it with his stick off Tootoo's left skate and past Mason for the 4-0 lead.
Nashville's lead could have been bigger. The Predators had two power plays late in the second, including 26 seconds with the 5-on-3 advantage, but couldn't get the puck past Pavelec.
Kostitsyn scored off a pass from Cody Franson for his second of the game and 22nd goal this season at 2:28 of the third. Wheeler converted a wrister at 3:06 to keep Rinne from posting a shutout, but Fisher's power-play wrister off a nice pass from Kostitsyn made it 6-1.
That's when Nashville coach Barry Trotz started spreading the ice time around, not worried about matching up against the Thrashers.
"They had their No. 1 line out, we had Blake [Geoffrion's] line out there," Trotz said. "That won't happen in the playoffs."
Forward J.P. Dumont was a healthy scratch for Nashville. ... The Predators improved to 40-4-2 when scoring three or more goals and 29-5-8 when scoring first. ... Kostitsyn extended his career-best points streak to 10 games. He has 13 points (six goals, seven assists) since March 17 for Nashville's longest such stretch this season. ... Atlanta scratched defenseman Tobias Enstrom (upper body) and forward Radek Dvorak (upper body), who did not travel with the team. ... The Thrashers had killed 15 straight penalties over the previous six games.