Mintyukov scored from the left hash marks off a cross-ice feed from Mikael Granlund.
Granlund had a goal and an assist, and Jacob Trouba and Mason McTavish also scored for the Ducks (21-13-2), who moved back into first place in the Pacific Division after losing four of the past five (1-3-1).
Lukas Dostal started for the second straight night after he gave up four goals on seven shots and was replaced in the first period of an 8-3 loss to the visiting Dallas Stars on Friday. He made 23 saves for the Ducks.
Mason Marchment scored in his first game with Columbus a day after he was traded to the Blue Jackets from the Seattle Kraken.
Dmitri Voronkov and Zach Werenski also scored and Elvis Merzlikins made 24 saves for the Blue Jackets (14-15-6), who have lost seven of eight (1-6-1).
Werenski scored his fifth goal in the past three games with a wrist shot from the left circle into the top left corner to tie it 3-3 at 12:44 of the third.
Werenski had to be helped off the ice after blocking a shot by Troy Terry with 2:27 left and that led to a penalty for too many men on the ice.
The Ducks took a 1-0 lead on their first shot on goal at 2:14 of the first period.
Anaheim defenseman Olen Zellweger, who was a healthy scratch for the first time this season in the loss to Dallas, brought the puck into the Columbus zone on a 3-on-1 rush and passed to Granlund, who scored for the third straight game with a wrist shot from the left hash marks.
The Ducks scored again 46 seconds later when Ryan Poehling spotted Trouba coming off the bench and slid a pass from the outside edge of the right circle to Trouba above the left circle for a one-timer to make it 2-0 at 3:00.
The Blue Jackets were on the first power play of the game when Charlie Coyle fed Voronkov at the far post and he redirected the puck across the goal line to cut it to 2-1 at 5:54 of the first.
Marchment deflected a shot from Damon Severson into the net to tie it 2-2 at 3:39 of the second.
After getting bowled over by Sennecke on a drive to the net and drawing a goalie interference penalty, Merzlikins kept the score tied when he stopped Jackson LaCombe on a short-handed 2-on-1 rush at 6:01.
The Ducks claimed a 3-2 lead at 13:36 of the second after Ross Johnston stole a pass from Dante Fabbro below the Columbus goal line just as McTavish came off the bench. Johnston backhanded a pass to McTavish and he scored with a wrist shot from the right hash marks.
