The shortened NHL schedule forced the teams to play for a third time in five days. Phoenix won the first two encounters in shootouts.
This is Hiller's sixth NHL season, all of them having been spent with Anaheim, and he now has 16 shutouts.
Jason LaBarbera suffered the hard-luck loss, stopping 23-of-23 shots. The Sharks had won two in a row.
Costly malfunction causes beer flood at Boston-area brewery
Megyn Kelly: Santa Claus and Jesus are both white men