Pavel Dorofeyev netted twice in the third period as the Golden Knights reached the third round of the post-season for the first time since they won their only Stanley Cup championship in 2023.
Mitchell Marner, Brett Howden and Shea Theodore also scored in what was a commanding triumph for Vegas.
Mikael Granlund netted Anaheim's only goal, as the Ducks failed to recover from another poor first period under coach Joel Quenneville.
The Golden Knights will now face the Colorado Avalanche in the Western Conference finals.