Mintyukov scored with a wrist shot from the left circle to move the Ducks ahead 3-2 at 16:52 of the second.
"He's a great offensive defensemen," Carlsson said of Mintyukov. "He's joining the rush a lot, so it's fun."
The Ducks could not capitalize on a 5-on-3 that lasted 1:09 early in the third period and Utah scored shortly afterward on a wrist shot from the slot in transition by Kesselring to tie it 3-3 at 5:21.
"We've just got to get pucks to the net, be a little more simple," Kesselring said. "We have a lot of skill, we want to make plays, but sometimes we have to dummy down a little bit and get pucks to the net."
Clayton Keller scored with a backhand from in close off a centering pass from Schmaltz to move Utah ahead 4-3 at 10:50.
"They thrive off turnovers and transition," Zegras said of Utah. "We knew it was going to be a little bit of a track meet. As much as we could, we tried to not play a track meet, but they're so young, skilled and fast that you just kind of have to respect their speed and stay to the inside and just play tough."
Zegras said the Ducks didn't get down after falling behind.
"We were playing good," he said. "I thought we were shooting the puck to the front of the net and we were utilizing the back of the net, trying to find guys in the slot."