Benn's four-point game gives him 87 for the season and the Art Ross Trophy as the NHL leader in points. Benn edged New York Islanders center John Tavares by one point when he got a secondary assist on Cody Eakin's goal with nine seconds remaining.
"What he did was special. That doesn't happen very often," Stars coach Lindy Ruff said. "To end up winning the League scoring [title], that's an incredible accomplishment. As a coach, you're proud to see one of your players accomplish that."
Two of Benn's goals came in the first period and the other was an empty-net goal with 2:05 left.
"My teammates gave a lot tonight and held the ice the last couple months and the whole year to get to the top, the scoring lead. I've got to thank them," Benn said.
Nashville (47-24-10), which lost its sixth straight game, got its lone goal from Filip Forsberg in the first period.
The Predators, who finished second in the Central Division, will face the Chicago Blackhawks in the Western Conference First Round. It is Nashville's first Stanley Cup Playoff appearance since 2012.
"I think guys are excited to get to the playoffs and open up in our building," Predators coach Peter Laviolette said. "It's an exciting time you work all year for."
Dallas (41-31-10) ended the season on a four-game winning streak but missed the playoffs for the sixth time in the past seven seasons.
"The No. 1 goal here is to make the playoffs and just give yourself a chance to win a Stanley Cup. We didn't do that this year and it's disappointing," Benn said. "It's going to be a long summer, a lot of time to think."
Benn gave Dallas an early lead with his 33rd goal of the season, a shot from the left circle 7:35 into the game. Benn received a backhand pass from Eakin and promptly scored with a flick over the glove of Predators backup goaltender Carter Hutton.
"What a way to finish … you see a guy win the scoring title," Stars defenseman Trevor Daley said. "It's a special thing to beat Tavares and (Pittsburgh Penguins forward) Sidney Crosby for the scoring title. I think those guys are the two best players in the game today. It's pretty special for that, but I guarantee you that (Benn) would have been happier with a playoff [appearance]."
Nashville tied it at 11:33 of the first when Forsberg scored his 26th goal of the season on a deflection. Forsberg was in front of the net and got his stick on a shot by Ryan Ellis from the slot.
Benn's second goal of the period exactly two minutes later gave Dallas the lead. With the Stars on a power play, Benn won a faceoff in the left circle against Paul Gaustad, sending the puck to John Klingberg, who was near the blue line.
Benn got his stick on Klingberg's shot, redirecting the puck top-shelf to Hutton's short side for his 34th goal of the season four seconds into the power play. Dallas gained the man-advantage after a tripping call on Viktor Stalberg at 13:29 of the first period.
"He's a first-class guy on and off the ice," Stars center Vernon Fiddler said of Benn. "At the end of the day, he's a guy that gets the job done. It's not easy to get more than a point a game in this League, especially where he's come from. He wasn't a first-rounder or your top pick that was a shoo-in for the top scorer of the League. He's worked for every inch he's got.”
Enroth made a huge save on former Stars center Mike Ribeiro at 10:10 of the third period, denying him at the far post as he was trying to score off the rush while shorthanded.
"I thought it was excellent," Ruff said of Enroth's performance. "He made probably three or four real big saves for us. There was two he made when the game was 2-1, which are difference makers."
Nashville trailed 2-1 heading into the third period and Laviolette felt the game was still there for the taking, at least until Benn's third goal of the game with 2:05 remaining.
"Well, there's some positives through the time up until we pulled the goalie," Laviolette said. "We kept pulling in the third. We had lots of chances to tie it up and push the overtime. Our guys kept pulling and fighting. It's unfortunate we couldn't tie it up. At this point, we're moving on and looking forward to Wednesday."
The Stars were without leading goal scorer Tyler Seguin, who was benched after being late to practice on Friday.
Hutton finished with 21 saves.
"Fortunately we've got a couple days to get back to work at practice, get our game in order and get our mind in order and get ready for a big challenge in Chicago," Predators center Matt Cullen said.