The Sharks, seeded No. 1 in the Western Conference, find themselves trailing 3-1 in the best-of-seven series and will try to find off elimination when they host the fifth game Saturday.
This was only the fourth playoff game of Hiller's career and he added a 29-save shutout to the blanking he recorded in the series opener eight days ago. Hiller replaced Jean-Sebastien Giguere as the team's No. 1 goaltender during the regular season.
Anaheim's Evgeni Nabokov matched Hiller in the first period, but Bobby Ryan scored twice in the second period to start the Ducks on their way to victory. They were the third and fourth goals of the series for Ryan.
Corey Perry and Drew Miller added third-period goals -- Miller's score going into an empty net.
San Jose came into the series having produced the best regular season in franchise history. The Sharks set club records in wins (53), points (117) and home victories (32).