Dutchman Sneijder rifled Inter ahead after 18 minutes and Japan's Yuto Nagatomo put them 2-0 up against the Croatian side just before the break.
Brazilian Philippe Coutinho completed the scoring in the second half of the third qualifying round first-leg tie.
"It's a good result but what I liked was the fact that we never stopped trying to play football and we gave very little away," Inter coach Andrea Stramaccioni said.
Inter are hoping to recover from a difficult last season when Stramaccioni, initially given the job on an interim basis, became the third coach to be employed by club president Massimo Moratti.
In other ties, Marseille were held to a 1-1 draw by Turkey's Eskisehirspor, Bundesliga side Hannover beat St. Patrick's Athletic 3-0 in Dublin and last season's beaten finalists Athletic Bilbao downed Croatia's Slaven Belupo Koprivnica 3-1 at home.