Andrew Ladd and Mathieu Perreault also scored for the Jets, who beat the Avalanche for the first time in four tries this season. Stafford also had an assist, and Michael Hutchinson made 32 saves for Winnipeg.
Stafford was positioned in the slot when he broke a 1-1 tie with his 15th goal of the season. Mark Scheifele got the puck behind the net and passed it cleanly through traffic to Stafford, who wristed it past goalie Semyon Varlamov.
Varlamov made 35 saves.
Winnipeg capitalized on a power play and built a two-goal lead on Stafford's second goal of the night -- a slap shot that found the net through Ladd's screen at 10:37 of the second period. Avalanche coach Patrick Roy tried to challenge that Ladd interfered with Varlamov, but it was not allowed.
Roy argued with referee Wes McCauley after his challenge was denied and was penalized for abuse of officials.
Duchene got the Avalanche within a goal when he scored at 14:12 of the second period on a wrist shot from the right side. It was his 24th goal of the season.
But the Jets scored again at 9:17 of the third on a breakaway. Perreault picked up a loose puck in the Jets' zone and streaked down the ice, pulling up between the circles and beating Varlamov with a shot over his right shoulder.
The Avs struck first when Grigorenko knocked in a rebound at 5:40 of the first while Colorado was on the power play. But the Jets evened the score as the first period wound down, in much the same fashion with Ladd getting hold of a rebound and driving it past Varlamov.
NOTES: A 5-minute fighting penalty in the first period pushed Cody McLeod's total penalty minutes this season to 101. He's the first player in the history of the Avalanche/Nordiques franchise to have more than 100 penalty minutes in eight different seasons. ... Jarome Iginla played in his 1,447th career game, snapping a tie with Tim Horton for 23rd place on the all-time list. ... The Jets will host the Avs in the fifth and final game of the season series between the Central Division rivals on March 12 at the MTS Centre. ... The multi-goal game by Stafford was his fifth of the season.