Matt Halischuk added a goal and an assist for Nashville, which jumped over Phoenix and Los Angeles and closed 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."
The Predators have 97 points with two games remaining. They need one point, or one loss of any kind by Dallas, to earn a berth.
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 3 assists.
Tootoo's three-point night was a career-best -- but 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."
Atlanta trailed 4-0 after two periods. Blake Wheeler scored twice in the third, and Nik Antropov added a late goal.
"We waited until a little too late to get our goofy things to happen for us and score some goals," coach Craig Ramsay said. "I can't blame anybody. When they got a chance, it went in."
Both teams had 12 shots in the first period, but the Predators did a lot more with their dozen against Chris Mason.
Halischuk opened the scoring at 5:24 with a backhander from the slot for his third goal. Tootoo got an assist on the goal, then made it 2-0 at 19:19 when took advantage of Antropov's failure to clear the puck from the crease after Mason had stopped Martin Erat's shot, flipping the puck over the goal line.
Kostitsyn made it 3-0 with 0.8 seconds left when he fired a wrister 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."
Rinne finished with 33 saves.
Ramsay changed goaltenders after Tootoo scored again at 1:56 of the second -- again taking advantage of a mistake by the Thrashers. 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.
Mason made nine saves before he was replaced by Ondrej 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."
Material from team media and wire services was used in this report.
1 - 0 NSH
2 - 0 NSH
3 - 0 NSH
4 - 0 NSH
5 - 0 NSH
5 - 1 NSH
6 - 1 NSH
6 - 2 NSH