Jannik Hansen scored the second of his two goals with 6:56 to go in the third, bringing the Canucks within one after they had begun the final period four goals down.
Jonas Hiller then shut the door on Vancouver, preserving a victory that ended Anaheim's six-game losing streak. The Canucks had won their previous two games.
All of Anaheim's goals came in the second period and the outburst began just 25 seconds into the stanza when Saku Koivu scored his second of the year. Andrew Cogliano and Corey Perry added power-play goals and Holland delivered his first goal of the season -- which eventually became the game-winner.
Kevin Bieksa began Vancouver's comeback bid 4:32 into the third and Hansen scored goals 3:52 apart to make Anaheim sweat out the victory.
Anaheim's goals were scored against Roberto Luongo, who was taken out of the contest after Holland's tally. Cory Schneider replaced Luongo and faced just two shots over the final 22 minutes.
Hiller made 38 saves to get the win. He faced 19 shots during the final period.