Ryan Miller saved 43 shots for his fourth 0, at Honda Center.
"I felt pretty good and I've been trying to be really calm in the net, and start from there in the crease," said Miller. "It helps that we have a lot of great back pressure and our 'D' is able to stand some guys up. I don't feel like I have to challenge the rush play as much and I can read what's coming."
Jonas Hiller was tagged for both goals on 24 shots for the Ducks, who have dropped their past two.
"For me, it's tough to be back there, feel like I'm playing pretty well and seeing the guys trying and trying and not getting anywhere," said Hiller. "It's definitely frustrating. If we play like that every night, we always have a chance to win."
Buffalo got the only goal it needed 7:12 into the game on the power play when Tyler Myers' shot from the right point went wide, but it bounced back to the left of the net and Roy shot it in.
At the 8:16 mark of the second, Buffalo increased its lead to 2-0 when Ehrhoff's shot from the high slot was tipped in by Boyes in front shortly after a penalty to Anaheim's Luca Sbisa expired.
Miller made double-digit saves in each frame as he stopped 10 in the first, 13 in the second and turned aside 20 in the third to post the shutout.
Buffalo continues its five-game road trip in San Jose on Thursday...Anaheim hosts Calgary on Friday...The Sabres have won three straight against the Ducks...Miller has 26 shutouts in his career.