The Sabres got within a goal of tying the score in the second period, but Hiller stood his ground and made 16 of his 41 saves in the third to help preserve a 5-4 victory on Tuesday night and extend Anaheim's home winning streak to eight games.
"We haven't been up 4-0 that often," Hiller said. "You want to keep going, but then you start going back a little bit on your heels than on your toes and it goes quick. The good thing is that we showed character and found a way to win."
Ryan Getzlaf and Evgeny Artyukhin scored 62 seconds apart to trigger a four-goal first, Bobby Ryan connected on a power play, and the Ducks also got goals from Mike Brown and rookie Troy Bodie in the only meeting between the teams this season.
The victory was the seventh in eight starts for Hiller.
Patrick Lalime made his seventh start of the season for Buffalo while Ryan Miller was rested before Thursday night's game at Los Angeles.
But Lalime, looking for his 200th NHL victory, allowed four goals on 11 shots in the first 10:26. That left coach Lindy Ruff with no choice but to switch goalies with a 4-0 deficit, after Lalime gave up Ryan's 22nd of the season. Miller stopped 18 of 19 shots in his first relief outing.
"Sometimes the strategy in changing goalies is to get the guys fired up, and we responded well," said Lalime, whose slashing penalty led to Ryan's goal. "It would have been easy to just pack it in. But everybody in this room was committed to come back. We responded well to the change and we came close."
Whatever Ruff told his players during the first intermission must have resonated. The Sabres, who scored a season-high seven goals in Monday's victory at Arizona, sliced the deficit in half with goals 28 seconds apart by Tim Connolly and Clarke MacArthur before the period was a minute old.
"Lindy told us that we had a chance to come back," Lalime said. "We were already on a power play, so he said 'Let's get one here, because you never know what can happen.' We showed a lot of character after being down 4-0, so you have to look at the positives. Everyone in this room never gave up and kept playing hard."
Connolly's 100th NHL goal, which extended his point streak to 13 games, came during a power play while Artyukhin was serving a roughing penalty. Artyukhin had gone after Sabres forward Patrick Kaleta, who had just leveled Ryan Carter with a vicious shoulder check at the red line just as he got rid of the puck in front of the players' benches in the final minute of the first period.
"It did change the momentum, but I'd rather have our players defending one another and take the penalty in that situation," Ducks coach Randy Carlyle said. "I thought Carter could have done a better job of protecting himself. He saw Kaleta coming and tried to stiff-shoulder him. But Kaleta's a pretty big guy who has been known to throw his body around, and he got the better of our play in that situation."
Buffalo's Steve Montador, who played 65 games with the Ducks last season, cut Anaheim's lead to 4-3 at 6:12 of the second when he intercepted a pass deep in the Ducks' zone and backhanded his third goal of the season past Hiller's stick.
"You can see why they've one of the top teams in the league," Carlyle said. "They've got an explosive offense and they can really hem you in your own zone. They have lots of confidence doing that, and we didn't do a good enough job of winning enough puck battles along the way when they applied that pressure -- particularly in the second period."
Bodie gave the Ducks an insurance goal with 4:07 to play. It came in handy, because Buffalo's Jochen Hecht scored with 53 seconds remaining.
The loss was the first for the Northeast Division-leading Sabres since a 5-2 defeat at Washington on Dec. 23. It dropped them two points behind the Eastern Conference-leading Capitals, following Washington's 3-2 home win against Detroit.
The Ducks, who won both meetings with Buffalo last season, set franchise records for the fastest two, three and four goals from the start of a game. Getzlaf began the scoring blitz just 51 seconds after the opening faceoff, converting a rebound for his 13th goal. Artyukhin scored his fourth goal on a breakaway, and Brown made it 3-0 at 5:23 of the first.
Anaheim is two wins away from matching the longest home winning streak in franchise history, which was set two seasons ago. The Ducks begin a six-game road trip Thursday at San Jose and don't return to Honda Center until Feb. 3 against Detroit.
Miller has made only one start against the Ducks. That was on Dec. 5, 2007 at Anaheim, when he played against his brother Drew for the first time in an NHL game and lost 4-1. Drew is now with Detroit. ... The Sabres have 12 goals over their past three games, with 11 different players scoring them. ... Buffalo's opponents were 2 for 44 on the power play over the previous 11 games. ... The Sabres are 15-2-6 in one-goal games.