Giguere, in his first season with the Avalanche, has 35 shutouts in his 14-year career but he did not have any during his 33 appearances with Toronto during the 2010-11 campaign.
Colorado snapped a three-game losing streak and handed the Stars their fourth straight setback. The Dallas skid has come after the Stars won 11 of their first 14 games.
Chuck Kobasew opened the scoring 6:10 into the first period and it remained a 1-0 contest until the Avalanche produced two power-play goals late in the third.
Kari Lehtonen made 42 saves for Dallas.