J.T. Miller converted a cross-crease pass from Horvat at 13:06 to make it 3-1, but Ryan Strome scored with 46 seconds left in the period to pull Anaheim to within 3-2.
Dakota Joshua scored on a rebound at 5:30 to put the Canucks ahead 4-2. Anaheim challenged the play for goalie interference, but the call stood after a video review.
The Ducks were then penalized for delay of game, and on the ensuing power play, Kuzmenko tapped in a backdoor pass from Pettersson at 5:54 to make it 5-2.
"The turning point was our challenge that went against us," Ducks coach Dallas Eakins said. "We wouldn't challenge it unless we thought it was goalie interference. … Obviously, the League saw it differently and we live with their call."
Max Comtois scored on a breakaway at 7:51 to make it 5-3, and Zegras scored on a long power-play shot through traffic at 13:35 to pull Anaheim to within 5-4.
However, Kuzmenko restored Vancouver to a three-goal lead with two his goals two minutes apart.
"When he scored, I didn't think it was a hat trick, and then I saw hats flying and we just got super happy for him," Pettersson said. "He's been working really hard. It's a new city and language and everything for him, so I'm just super happy for him."
Max Jones scored on a rebound with 2:22 left to cut it to 7-5, but Horvat scored his team-leading 10th goal into an empty net with 55 seconds left for the 8-5 final. Horvat has six goals during a three-game goal streak.
"We've got to do a better job of limiting those grade-A chances," Zegras said. "[Gibson] gives us a chance to win every night and I guess to have that kind of result [stinks] for us because of how big of a part of the team he is."
NOTES: Miller has seven points (four goals, three assists) in a five-game point streak. … It was the third five-point game of Pettersson's NHL career, tying him with Alexander Mogilny for the Canucks record. … Martin is 2-0-1 this season and 5-0-4 in his past nine games, passing Curt Ridley (1975-76) for the most consecutive games earning at least a point after joining the Canucks in their history.