The Avalanche got only one shot in the third period, however, and one more in overtime.
"In a perfect world, you'd like to jump out to a 2-0 or 3-0 lead, and by the end of the game snuff them right out and not give them anything," Boudreau said. "But if you look at our third periods lately, when we're tied or behind, we don't allow the other team much in the third. The third period is the most important period, and tonight we allowed one shot."
Giguere, the Ducks' career leader in games (447), wins (207) and shutouts (32), kept the Ducks at bay during a 53-second, 5-on-3 power play early in the second period.
He stopped their first 12 shots before Perry converted Getzlaf's centering pass at 6:59 of the second. Selanne then scored his fifth goal while Colorado's Jan Hejda served a charging penalty.
"They have some players that can put the puck in the net," Giguere said. "That power play is a golden opportunity for them, and that's a lesson we can learn because a good team will find a way to win on those types of power plays.
"That's the type of attitude and killer instinct we need to have."
Mitchell halted Anaheim's momentum 40 seconds later, using newly acquired defenseman Ben Lovejoy as a screen and beating Hiller from the slot to put the Avalanche back in front.
Colorado opened the scoring at 2:28. The Ducks, who came in with the second-worst penalty-killing percentage in the NHL (74.1), fell behind 2-0 after center Nick Bonino received a double minor for cutting Chuck Kobasew with a high stick at 9:42 of the period.
Parenteau cashed in with 48 seconds left on Bonino's penalty, converting a rebound of Tyson Barrie's slap shot. It was Parenteau's eighth goal and first in eight games, after a three-game stretch in which he scored four times.
"There is a reason why (the Ducks) took a few penalties in the first period. We were quick to the puck, moving our feet and we were physical," Colorado coach Joe Sacco said. "We got ourselves a good lead there, but then we got ourselves into a little penalty trouble.
"It was a hard-fought game, and it was disappointing that we couldn't get the extra point."
NOTES: The Ducks are the first NHL team to win six consecutive games when trailing in all six since Columbus did it from March 24-April. 3, 2006. ... Selanne's goal was his 35th against Colorado, the eighth team he has reached that figure against. He played one season for the Avalanche (2003-04) and scored 16 goals before returning to the Ducks. ... The Ducks are 18-4-1 against Colorado since a 2-0 road loss on Feb. 13, 2007. ... Anaheim D Cam Fowler returned to the lineup after missing eight games because of a head injury.