It was the home opener for the Ducks, who improved to 3-1 with a one-sided decision that brought Hiller the 17th shutout of his seven-year career.
New York has dropped three of its four games, all of them having been played on the road. The Rangers are opening their season on a nine-game road trip. They will not play their first home game until Oct. 28.
Silfverberg produced the second of Anaheim's three goals in the first period and he opened the scoring in the middle stanza with a slap shot. They were his third and fourth goals of the season.
Hiller made 34 saves while Henrik Lundqvist let in all six Anaheim goals on 38 shots.