The start was Hiller's fourth in a row and third victory in that stretch. He's started six of Anaheim's last seven, posting a 4-2 record.
Giguere's father died in mid-December, and since the goalie came back, he's played fewer games than usual and been relatively inconsistent when he has been between the pipes. Ducks coach Randy Carlyle said he wanted to give Giguere some time and some space to get his game back in order, thus Hiller gets the nod.
"We think this is the best route to take in this situation, and we're going to live with it," Carlyle said. "It's not like he [Giguere] is not going to play for our hockey club again. He's going to get his opportunity.
"As I've said, we have 1A and 1B. Jonas Hiller's come in and given us the goaltending that's necessary to have some success the last little while, but we're not afraid to go back to Giguere. He knows he's going to get his opportunity."
Hiller said he was surprised to be getting so many starts.
"You never hope that the other guy's struggling or anything. But as a backup, those are when you get the chances, and I know that," Hiller said. "So I'm going to try to keep it up.
"You can see Jiggy's not happy the way he's played and not happy that he's not getting a lot of starts right now, but he's not angry at me. He still supports me and helps me if I need anything. So it's awesome to work together with him."
Kunitz scored on a power play early in the period and Perry gave the Ducks a two-goal lead on another man-advantage midway through the third. Chris Pronger also scored for Anaheim.
Buffalo pulled within one when defenseman Craig Rivet scored with 6:33 remaining.
"We have to find ways to win those third periods," said Sabres center Paul Gaustad, who had two assists. "We kind of sat back on our heels. We passed up a lot of shots, so that is something we have to be better at."
The Sabres have four defensive regulars sidelined, which probably had something to do with the difference in shots. Buffalo took just 23 to the Ducks' 37.
"You look at our defense and you might think there is going to be a shot disparity," Sabres coach Lindy Ruff said. "I didn't like our skill guys tonight; they didn't get enough done for us. There wasn't much coming from the top.
"The guys down below were getting most of the work done."
Perry's goal turned out to be the difference. Buffalo's Patrick Lalime slowed a shot, but the puck got past him and was sitting behind him in the crease. Perry then reached around and tapped it in for his 17th goal.
Rivet knocked in a rebound for his first goal of the season.
Andrew Ebbett and Kunitz combined on a bang-bang play early in the third period to give Anaheim a 2-1 lead while Rivet was serving a slashing penalty. Ebbett controlled the puck directly behind the Buffalo goal, then snapped a pass to Kunitz, bearing down on Lalime from the right side. Kunitz slid the puck between the goalie's pads for his 14th goal.
Patrick Kaleta scored Buffalo's first goal, 13:17 in. It was his third.
The Ducks were 2-for-3 with the man advantage. ... Anaheim C Samuel Pahlsson missed the game with flulike symptoms. ... The Sabres just recalled D Mike Weber from AHL Portland. Among the four missing defensive regulars for Buffalo is Jaroslav Spacek, who hurt his hip in a 2-0 win at Phoenix on Saturday. ... Rivet's goal ended a 65-game drought dating back to Jan. 12, 2008, when he scored for the San Jose Sharks against Toronto's Vesa Toskala. Rivet has 46 goals in 777 NHL regular-season games.