Nashville (52-18-11) clinched the Central Division and Western Conference and will have home-ice advantage for as long as it plays in the Stanley Cup Playoffs.
Craig Smith scored twice, and Ryan Johansen scored the tiebreaking goal at 14:33 of the third period for the Predators, who set their record with 52 wins. Nashville will play the second wild card into the Stanley Cup Playoffs from the Western Conference in the first round.
WATCH: [All Predators vs. Capitals highlights]
"It's a pretty good night for us, for sure," Predators defenseman Roman Josi said. "It's such a tough league, and I think it's something we take a lot of pride in. We worked hard all year for this. Obviously, the big goal remains to win a Stanley Cup, but it's definitely something we're proud of."
Alex Ovechkin scored his NHL-leading 47th goal for the Capitals (48-26-7), who have won the Metropolitan Division and will play the first wild card from the Eastern Conference.
Ovechkin needs a hat trick in the regular-season finale against the New Jersey Devils on Saturday to reach 50 goals for the eighth time. He leads Winnipeg Jets forward Patrik Laine by three goals for the Rocket Richard Trophy, which Ovechkin has won six times.
"Right now our focus is not on 50, our focus is on the playoffs," Ovechkin said. "And being in shape. We didn't get hurt. That's the most important thing."
Josi scored a power-play goal for Nashville at 8:19 of the third period to tie it 3-3.