Raddysh and Nikita Kucherov each had a goal and an assist, and Hagel had three assists for the Lightning (23-13-3), who have won five straight. Andrei Vasilevskiy made 25 saves.
Jon Cooper, who appeared in his 1000th career game as a coach with Tampa Bay, recorded his 595th win (595-319-86), which is the second-most by any coach in their first 1,000 games coached, trailing only Hockey Hall of Famer Scotty Bowman (598). Cooper is also the fifth coach in NHL history to reach 1,000 games for one franchise.
"I can't imagine what the video looks like from Game 1 to what I look like now at 1,000," Cooper said. "It's interesting because I've been a part and been able to watch players in our organization hit the 1,000 milestone, whether it's in games or in points, and you just kind of sit back and you marvel at what it took for that player to get to that point. You never really put yourself in that spot, and when you get hired you're not sitting there thinking, 'I wonder what game 1,000 will be like.' You're sitting there thinking, 'God, I hope I can get to another contract.' "
Jansen Harkins, Beckett Sennecke and Mason McTavish scored for the Ducks (21-16-3), who have lost a season-high four in a row (0-3-1). Dostal made 25 saves.
“It was really tight-checking," McTavish said. "Kind of felt like a playoff game. Not many chances, so every mistake really mattered. It’s fun to play in those games and obviously would have been better if we came out on top.”
Brayden Point appeared to give the Lightning a 1-0 lead on a redirection at 8:41 of the first period, but Anaheim challenged the play for being offside and the goal was overturned following a video review.
Tampa Bay took a 1-0 lead at 13:30 after Raddysh faked a slap shot and passed to J.J. Moser in the left circle. He briefly held onto the puck to avoid a block and then shot it under the glove and over the left pad of Dostal.
The Ducks had two prime scoring chances early in the second, but Sennecke hit the crossbar on a breakaway at 4:20 and Leo Carlsson was stopped by Vasilevskiy at the end of 2-on-1 at 5:08.
Anaheim tied it 1-1 at 15:17 after Lightning defenseman Charle-Edouard D'Astous lost the puck just before exiting his zone. Ross Johnston took possession for the Ducks and slid the puck over to Harkins, who finished the 2-on-1.
Tampa Bay moved back ahead 2-1 with 49 seconds left in the second when Maxwell Crozier fed Point at the far post, where he redirected the puck into an open net behind Dostal.
The Ducks tied it 2-2 at 3:57 of the third period when Sennecke brought the puck out of the corner and scored short side from the left circle.
Kucherov gave the Lightning a 3-2 lead with a power-play goal at 8:00, scoring with a one-timer from the right circle for his fifth goal in the past three games.
