Anaheim scored three times in the second period to erase a 2-0 deficit.
Vatrano scored his team-leading 18th goal of the season over Silovs' glove on a one-timer from the left circle to cut it to 2-1 at 5:27.
Gauthier also scored over Silovs' glove from the same spot as Vatrano, but off the rush, to tie it 2-2 at 9:09.
"He's a gamer," Strome said of Gauthier. "He can look like he's not involved in the game and, next thing you know, you see his speed and his shot and he's got that game-breaking ability."
Strome gave the Ducks a 3-2 lead at 18:41 when he scored with a wrist shot from the slot off a centering pass from Mason McTavish.
LaCombe scored with a wrist shot off the rush with 4:14 left in the third period during 4-on-4 play to extend the lead to 4-2.
"We need some guys to rise to the occasion, whether that's a middle drive or going to the net," Tocchet said. "We had shots on net with nobody going to the net, so a little disappointed in the grit part of our game."
Terry scored into an empty net with 2:06 left for the 5-2 final.
"It was just simplifying our game in the second and third and we just kept rolling them over," Strome said. "Everyone did a great job. The bench was really ready to go. Everyone was on their toes. It seemed like every line was generating momentum and that's a good sign."