Kucherov became the 101st NHL player to achieve the milestone and joined Steven Stamkos as the only players in Lightning history to get 1,000 points. He is the third-fastest active player to hit the mark (809 games), behind Edmonton Oilers center Connor McDavid (659) and Pittsburgh Penguins center Sidney Crosby (757).
Anthony Cirelli had two goals and an assist, and Jake Guentzel scored twice for the Lightning (2-4-2), who had lost four in a row and lost their first three home games. Victor Hedman and Brandon Hagel each had two assists, with Hagel getting his 800th NHL point, and Jonas Johansson made 37 saves.
Troy Terry had a goal and an assist for the Ducks (4-3-1), who were 2-0-1 in their past three games. Lukas Dostal made 29 saves.
Cirelli scored the game-winner on the power play at 16:45 of the third period. He scored with a wrist shot from the left hash marks off a pass from Kucherov.
Anaheim had tied the game in the third with two goals in 59 seconds.
Ryan Poehling made it 3-2 at 7:11 when he finished off a 2-on-1 by tapping the puck past Johansson off a pass from Ross Johnston.
Terry then tied it at 3-3 at 8:10, scoring from the inside edge of the left circle off a pass by Cutter Gauthier.
Guentzel gave the Lightning a 1-0 lead at 9:10 of the first period, scoring on the rebound of his initial shot from the right circle.
Jacob Trouba tied it 1-1 at 4:42 of the second period, sending a slap shot from the right circle past Johansson to the short side.
Guentzel put the Lightning ahead 2-1 at 12:19 when he redirected a Brayden Point pass with his skate. Kucherov had the secondary assist for his 1,000th point.
Cirelli extended the lead to 3-1 at 14:20, tapping in a rebound at the edge of the crease.
Ducks forward Mikael Granlund left the game after the first period with a lower-body injury.
