Avalanche center Matt Duchene nearly scored on a short-handed breakaway but was slashed by Phaneuf.
Giguere came off for an extra skater with 2:56 left, and Toronto center Jay McClement scored into the empty net less than a minute later.
"We lost the game in the second period," MacKinnon said. "Their goalie made some good saves for them. We've been playing well of late, but we can't let this game get us down too much."
NOTES: The Avalanche activated RW P.A. Parenteau and D Nate Guenin from injured reserve. Parenteau, who missed 10 games with a sprained left knee, was in the lineup. Guenin was scratched. ... The Maple Leafs' last six-game winning streak was Dec. 23, 2005 to Jan. 2, 2006. ... Colorado honored referee Brad Watson before the game. Watson was officiating in his 1,000th NHL game. ... D Dion Phaneuf owns the Toronto records for most games played (38) and assists (15) against Colorado. ... Avalanche LW Alex Tanguay (hip) missed his 36th game, but he has been skating. He could return to the lineup as early as Friday, when Colorado plays the Panthers in Florida.