Teravainen made it 3-1 at 13:52 of the second period. He batted down an errant shot with his stick before scoring short side on Dostal from the right circle.
Vatrano responded for the Ducks to push it to 4-1 at 16:44, shooting blocker side from the right circle off a pass from Strome from below the goal line.
Teravainen scored his fourth goal of the season on a slap shot from just inside the blue line during a power play to cut it to 4-2 at 3:01 of the third period.
Martin Necas then cut it to 4-3 at 15:29 with his own power-play goal, tapping in a backdoor pass from Michael Bunting.
However, Fowler (18:03) and Vatrano (18:41) each scored into an empty net for the 6-3 final.
"We knew they were going to come in the third," Cronin said. "To me, the big positive in that is we kept them to the outside and we had a lot of blocked shots and we won the game, so that's going to be a lot of third periods. Obviously, it's a style in the NHL, people throw everything at you, and I thought we did a good job weathering the storm."
NOTES: The Ducks have won three straight against the Hurricanes and are 16-4-1 in their past 21 games against them. ... Anaheim has won eight straight home openers, which is tied with the Toronto Maple Leafs and Boston Bruins for the longest active streak in the NHL. ... Strome's assist on Mintyukov's goal was his 400th NHL point. ... LaCombe's assist on Mintyukov's goal marked the fifth time in NHL history that a defenseman has scored his first NHL goal off an assist from another defenseman who recorded his first NHL point.