Getzlaf produced his seventh goal of the season as the Ducks won for the fifth time in their last six games.
Anaheim's Pontus Aberg scored with 3:50 remaining in regulation. His shot bounced off Carolina goalie Curtis McElhinney's shoulder and into the net.
Goalie John Gibson stopped 33 shots for Anaheim.
Andrei Svechnikov scored in the first period for Carolina, which had won four of its previous five games.
McElhinney made 27 saves. His record dropped to 7-3. He had never started in as many as nine games prior to December in a season, yet he emerged as the team's top goaltender over the past couple of weeks.
The Ducks have won in their last five trips to Raleigh.
Anaheim is 3-1-0 so far on a five-game road swing.
The Hurricanes, who will not play at home again until Dec. 11, went 0-for-6 on power plays.
Gibson stopped the first 18 shots he encountered, including a few that could have frustrated the Hurricanes.
Then Svechnikov cut through the upper part of the slot and unleashed a shot that Gibson could not handle with 1:03 to play in the first period. It was the rookie's sixth goal of the season.
The Hurricanes held a 21-6 edge in shots on goal through the first period.
By the midway mark of the second period, the Hurricanes were 0-for-4 on power plays. In two chances with man advantages early in the second period, Carolina produced only one shot. The Hurricanes were denied on two more power plays in the third period.
The teams will meet again next Friday night at Anaheim, Calif.
Earlier in the day, the Hurricanes announced that Micheal Ferland, the team's top goal scorer, had a concussion and would miss the game. Plus, Carolina had a roster adjustment with goalie Scott Darling cleared waivers and was assigned to the Charlotte Checkers of the American Hockey League.
(With inputs from agencies.)