Tuch collected Jordan Kyrou’s feed from below the goal line and rifled a wrist shot from the left face-off dot over Juuse Saros’ blocker to break a 3-3 tie with his 10th of the season.
The 30-year-old forward has five goals on a three-game goal streak and leads the NHL with five game-winning goals.
Cole Hutson had his first two-goal game in the NHL for the Capitals (8-4-0), who won 5-2 against the Philadelphia Flyers on Wednesday. Aliaksei Protas and Jack St. Ivany each had two assists, and Charlie Lindgren made 24 saves.
Alex Ovechkin had three shots on goal in 10:56 of ice time in his final regular-season game at Bridgestone Arena
Filip Forsberg scored two goals, Roman Josi had three assists, and Saros made 25 saves for the Predators (4-4-5), who are 2-3-4 in their past nine games.
Forsberg put the Predators ahead 1-0 during a 5-on-3 power play at 12:48 of the first period. He one-timed Josi’s cross-ice feed from the left face-off dot, scoring on the power play for the third consecutive game.
Hutson tied it 1-1 at 16:13, pinpointing a wrist shot from the bottom of the right circle to beat Saros on the near side.
Boone Jenner gave the Capitals a 2-1 lead at 4:15 of the second period. After winning a face-off, Jenner followed Martin Fehervary’s shot from the point and wristed the rebound past a screened Saros.
Forsberg evened the score 2-2 at 9:09 when Josi swatted a loose puck toward the crease, where Forsberg picked it up and maneuvered around Lindgren for an open look at the net. Forsberg has seven points (four goals, three assists) in his past three games.
Huston roofed a snap shot under the crossbar to put Washington back in front 3-2 at 13:46.
Ross Colton continued the back-and-forth battle by tying it 3-3 on Adam Edstrom’s rebound at 6:34 of the third period.
