Nashville had a 2-0 lead heading into the middle period, but Getzlaf delivered two goals in the first 4:36 of the stanza.
The Predators regained the lead on a goal by Richard Clune, but by the end of the second period Anaheim was in front thanks to Corey Perry and Teemu Selanne. Perry's goal was his 25th of the season, tied for second most in the NHL behind the 31 scored by Alex Ovechkin.
Frederik Andersen blanked the Predators over the final period and picked up the win with 23 saves. Marek Mazanec allowed four goals on 28 shots.
Anaheim won its fifth in a row and became the first team in the NHL to reach the 70-point plateau.