Inter coast to Europa League win in Croatia
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, a second-half strike from Stewart Downing gave Liverpool a 1-0 win away to Belarus side Gomel and last season's beaten finalists Athletic Bilbao beat Croatia's Slaven Belupo Koprivnica 3-1 at home.