The two have combined to allow two goals in helping Anaheim win three straight heading into Sunday's game against the Carolina Hurricanes.
With Giguere back in his native Montreal attending to a personal matter, Hiller made 26 saves and earned his second career shutout - and second in his last four appearances - in a 1-0 victory Friday over visiting Chicago.
"Sometimes you have to be lucky," said Hiller, who had his first career shutout against Los Angeles on Nov. 16. "They had two or three open nets, and they missed all of them. All I did was try to put something there so the players had to think where they were going to shoot. Sometimes that's enough to make them miss the net."
Giguere is expected to rejoin the Ducks (13-8-3) Sunday in Carolina, but with the way Hiller has played of late, they might not need him.
The second-year goalie is 4-0-0 in his last six appearances and has stopped 131 of the last 138 shots he has faced. Hiller is also among the league leaders with a 2.07 goals-against average and a .929 save percentage.
He has never faced the Hurricanes (12-10-2), but Giguere has faced them six times, going 1-3-0 with one tie. His lone win came Feb. 9, 2003, in Anaheim.
Giguere had lost five straight before a 4-1 victory Monday over Colorado. He has experienced an up-and-down season, starting 1-4-0 before winning six straight, and his 3.01 GAA is his highest in the past 10 years.
Ryan Getzlaf, Anaheim's leader with 28 points, scored Friday to extend his point streak to seven games. Getzlaf has three goals and six assists during the streak.
The Hurricanes broke a three-game losing streak Friday when Sergei Samsonov scored with 1:07 left in overtime to give the team a 3-2 win in Philadelphia.
Carolina gave up the first goal for the ninth straight game, but unlike the three previous contests, the Hurricanes rallied to take the lead as Pat Dwyer scored his first career goal 15 minutes into the second period and Tuomo Ruutu followed 76 seconds later.
Carolina gave up the tying goal with 46 seconds left in the period, but outshot the Flyers 15-7 over the final 20 minutes and overtime.
"Every game seems to be a battle for us," Samsonov said. "We've been playing from behind a lot lately, so it's not a good thing. We try to stay positive."
Carolina's offensive struggles have played a part in those early deficits. The Hurricanes' three goals Friday marked just the third time in the last 12 contests that they have scored more than twice.
Carolina has also converted just 13.4 percent of its power-play chances, going 0-for-21 over its last five games.
The Hurricanes have won three straight over the Ducks, but have split the last four meetings at home.