Hiller thwarted three power plays en route to his fourth shutout of the season, the 10th of his career and first against San Jose. He stopped 27 shots in a 6-0 win over Columbus on Friday.
"We didn't score as many goals as the last one and I absolutely did not want to get scored on , said Hiller, who hasn't allowed a goal in 150 minutes and 50 seconds. "It worked out well again. I think everybody feels good out there and so do I. We had a great team effort. It was just a 1-0 game, but we created lots of chances and played a lot in their zone, especially in the third."
The Sharks have just five goals over their last five games since beating the Stanley Cup champion Chicago Blackhawks 5-3 on Dec. 30. They have taken 129 shots on net over their last 13 periods of hockey, but have just one goal to show for it.
"We are playing good hockey but nothing wants to find its way in the net for us right now," said Sharks captain Joe Thornton. "We are right there, right on the brink of breaking out. We've just got to keep working at it, because it is tough to score goals. We are getting a lot of chances, but we have to keep our heads up and keep fighting."
Sharks rookie forward Logan Couture hit the right post with a 30-foot wrist shot in the first period and was stopped by Hiller twice from short range about a minute into the second period.
Ryan opened the scoring at 14:29 of the second period with his team-high 18th goal. He stickhandled across the slot waiting for an opening, then beat Antti Niemi from a sharp angle to the right of the net after Sharks defenseman Marc-Edouard Vlasic steered him in that direction. Niemi finished with 27 saves.
Ryan's goal was his fourth goal in five games since shifting from right wing to center in the wake of captain Ryan Getzlaf's injury. Getzlaf was struck by a deflected puck at Phoenix, breaking several bones in his face and sidelining him for more than a month.
After the win, though, Ryan directed all the accolades in Hiller's direction.
"He made crucial saves, especially at the end of the second when they could have changed the entire momentum of the game," Ryan said. "Like we've all said so many times, he's a rock back there for us. We certainly appreciate it. Another shutout is well deserving for him."
The Sharks, who didn't have to use their penalty-killing unit at any point in their 2-1 loss to Nashville on Saturday, didn't get their first penalty against the Ducks until Jamal Mayers was sent off for tripping Luca Sbisa with 10:11 left in the third period.
San Jose has three scheduled games remaining against its Pacific Division rivals, including two of their final five regular-season contests. The next meeting on Feb. 2 at Anaheim will be the 100th between the clubs.
Anaheim has gone 4-1-0 thus far in the six-game homestand, set to conclude Wednesday against the St. Louis Blues.
"The games have been emotional," Ducks coach Randy Carlyle said. "These are hard-fought games. There is not a lot of space on the ice. You have to compete for your space. Situations we've been presented with, we've shown a lot of battle."
Material from wire services and team media was used in this report.