It was the first hat trick of Getzlaf's nine-year career.
The Ducks sent 46 shots on goal and finally drove Ryan Miller from the game after he had given up six scores on 34 shots. Jonas Enroth came in for Miller to start the final period.
Getzlaf opened the scoring with a power-play goal 2:11 into the contest and then tallied twice more during the final four minutes of the first stanza.
Cam Fowler also scored for the Ducks in the first to give them a 4-1 lead at the end of the period.
Frederik Anderson picked up the easy win, his fifth of the season without a loss, by making 25 saves.
The Sabres have won just three times in their 19 games.