The 20-year-old Mintyukov finished in the top-five among rookie blueliners in in points (third), assists (third), goals (tied fifth), power-play points (tied third) and shots (fourth) last season.
With an assist, Brian Dumoulin recorded his first point as a Duck.
McTavish's two second-period assists secured his 45th career multi-point game in the NHL, and his 20th game with multiple assists.
Carlsson would come millimeters from doubling that lead early in the third, beating Ingram clean with a power-play wrister, but the shot rang the crossbar and bounced out of play.
That bad break would quickly come back to haunt the Ducks, as when the power play ended, Kesselring finished an odd-man rush the other way while Anaheim attempted a line change.
Anaheim's Isac Lundestrom left the game in the third period following a hit to the head by Utah's Nick Schmaltz. Lundestrom did not return. Schmaltz was not penalized on the play.
Keller would score the decisive goal on a pass from Schmaltz shortly after his linemate's hit, tucking a backhand bid inside the post off the rush.
Anaheim would refuse to go down without a fight though, and this time with some fortunate home cooking. With the Ducks on the rush, Brock McGinn's shot from the high slot was blocked right to Mintyukov at the side of the net. The young defenseman tried to sweep a rebound bid towards the goal, but instead had his shot bounce off the goaltender's leg pad and just barely far enough over the goal line to tie the game for the fourth time tonight.