Brandon Hagel sent a backdoor pass to Raddysh, who lifted a shot over Lukas Dostal's glove as he drove the net.
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 24 saves.
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 24 saves
Brayden Point appeared to give Tampa Bay a 1-0 lead a redirection at 8:41 of the first period, but Anaheim challenged for offside and the goal was overturned following a review.
The Lightning 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 break at 5:08.
Anaheim tied it 1-1 at 15:17 after Tampa Bay 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.
The Lightning 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.
McTavish tied it 3-3 at 13:02 while on a power-play with a wrist shot from the slot past Vasilevskiy's blocker.
