The Swiss goalie matched the Anaheim record with 51 saves, and turned aside three shootout tries in the Ducks' 3-2 victory over the Oilers on Friday night.
"Sometimes it's better to have a lot of shots than just a couple, so it was easy to find my game and easy to be in the game and it felt good," Hiller said.
Corey Perry scored in regulation and added the shootout winner in the Ducks' first game on a five-game trip. Rob Niedermayer added a short-handed goal to help the Ducks improve to 18-12-3 with their fourth victory in six games.
Hiller, in goal with Jean-Sebastien Giguere on leave in Montreal following his father's death, tied the franchise saves record set by Mikhail Shtalenkov against Ottawa in March 1998 and matched by Giguere against Detroit in March 2004.
"He was amazing," Ducks captain Scott Niedermayer said. "We were in the box way too much and he came up huge on a bunch of saves when we were trying to kill penalties and then obviously in the shootout. He won it for us there."
Anaheim coach Randy Carlyle agreed.
"He gave us a chance to win and obviously he was the best player on the ice and that's what you need sometimes when you go out on the road," Carlyle said.
Kyle Brodziak and Eric Cole scored for Edmonton. The Oilers have lost three straight to fall to 14-14-3. They're 4-5-3 at home.
"You have to take some confidence away from battling back like that," Oilers forward Shawn Horcoff said. "It was a character point for us tonight."
Oilers coach Craig MacTavish admitted it was tough to see the extra point slip away at the end, but was happy they even had an opportunity to win it.
"It sure ended up a lot better than it looked like it was going to," macTavish said. "It looked like it was a train wreck in the process."
Anaheim star Teemu Selanne cut his left thigh in the first period when he took a hit along the boards from Denis Grebeshkov. Selanne had to be helped off the ice and did not return to the game. He'll have an MRI in Anaheim on Saturday.
"It's a deep cut, but we don't think it is any where near what Corey Perry had a year ago where he missed six weeks," Carlyle said.
Perry gave the Ducks a 2-0 lead midway through the second period, tipping a shot past Dwayne Roloson on a power play.
Edmonton outshot Anaheim 21-4 in the third period, tying it on Brodziak's goal at 6:32 and Cole's power-play strike at 13:57.
Hiller is 7-5-1 with a 2.07 goals-against average. ... Selanne played in his 1,100 NHL game. ... Anaheim recalled goalie David LeNeveu from Iowa of the American Hockey League to back up Hiller.