Carlsson has three goals and six assists in a five-game point streak.
Troy Terry had two goals and an assist, Cutter Gauthier had two assists and Lukas Dostal made 27 saves for the Ducks (6-3-1), who have won four of five. Terry extended his point streak to six games (10 points; five goals, five assists).
Lucas Raymond and Alex DeBrincat each had a goal and an assist for Detroit (8-4-0), which was coming off a 4-3 shootout win at the Los Angeles Kings on Thursday. DeBrincat has scored in four straight games.
John Gibson made 27 saves in his first return to Anaheim since he was traded to the Red Wings on June 28 after 12 seasons with the Ducks.
Anaheim scored shorthanded for the second straight game when Terry got loose on a breakaway for a 1-0 lead at 4:53 of the first.
Detroit killed Anaheim's first power play and scored 48 seconds later when Dylan Larkin passed the puck ahead to Raymond, who went through the five-hole to tie it 1-1 at 8:19.
Terry led a 3-on-2 rush before making a cross-ice pass to Carlsson, who scored with a wrist shot from the left circle for a 2-1 lead at 12:24.
Detroit defenseman Moritz Seider appeared to score on a rebound at 4:57 of the second, but the Ducks challenged that Seider used a kicking motion to score the goal and it was disallowed after a video review.
Mason McTavish scored at 6:35 to extend the lead to 3-1. He received a pass along the wall, skated the puck to the opposite side and scored with a wrist shot from the right circle through traffic.
The Red Wings were on a power play when DeBrincat received a pass to the side of the net, turned and scored from in close to cut it to 3-2 at 15:25 of the second.
The Ducks were on a power play in the opening minute of the third period when Chris Kreider scored with a backhand just after Gibson had knocked the net off its moorings. The goal was awarded and then confirmed after a brief review, giving the Ducks a 4-2 lead at 55 seconds.
Terry scored into an empty net with 2:32 left for the 5-2 final.
