Sneaking up the left wing, Stastny made a nifty move to elude two Sabres defenders. He went around the net to set up Milan Hejduk's one-timer from the right circle 10 minutes into the game. The short-handed goal lifted the Avalanche into a 1-1 tie with the Sabres.
Stastny then added an assist on Brett McLean's goal 12 seconds into the second period, giving Colorado a 2-1 lead.
Stastny, who has eight goals and 25 points during the streak, tied the rookie mark set in 1993 by Winnipeg's Teemu Selanne.
Stastny also set the franchise rookie record, breaking the 16-game mark set by his father, Peter, in 1980 with the then-Quebec Nordiques.
The 17-game streak is the longest in the NHL this season, and the best run since Ottawa's Dany Heatley had a point in 22 consecutive games from Oct. 5 to Nov. 29, 2005.