Drouin scored twice and had an assist, MacKinnon had a goal and two assists and Justus Annunen made 44 saves to help Colorado (48-22-6) move three points behind the first-place Dallas Stars in the Central Division.
Vinni Lettieri and Declan Chisholm scored, and Filip Gustavsson made 30 saves for Minnesota (36-30-9), which has lost two of three.
Artturi Lehkonen put the Avalanche ahead 1-0 at 4:34 of the first period off a rebound after Gustavsson was unable to cover Jack Johnson's shot from the point.
Lettieri answered back and the Wild tied it 1-1 at 8:05 with a one-timer from the right circle off a behind-the-net pass from Mason Shaw.
Drouin put Colorado back on top 2-1 with a power-play goal at 12:28, batting in Cale Makar's shot from the blue line. He increased the Avalanche lead to 3-1 43 seconds into the second with a tip-in at the backdoor off a MacKinnon shot.
Chisholm pulled the Wild within 3-2 at 10:10 on the power play with a point shot from the left side.
MacKinnon scored his 48th goal of the season on a partial breakaway to make it 4-2 at 6:32 of the third.
Mikko Rantanen scored into the empty net at 18:32 for the 5-2 final.
