Hillis was signed Wednesday after numerous injuries to the New York rushing corps and he responded with 36 yards on 18 carries, including a 1-yard scoring run that put the Giants ahead 17-7 in the third quarter.
The former Cleveland Browns back also made five catches for 45 yards as New York (1-6) snapped a six-game losing streak starting the season.
Eli Manning completed 23-of-39 passes for 200 yards without an interception and hurled 24-yard touchdown toss to Rueben Randle, taking advantage of three Minnesota turnovers.
Ex-Tampa Bay quarterback Josh Freeman, signed by the Vikings Oct. 7, struggled under center in his first game for Minnesota (1-5), making good on just 20-of-53 attempts for 190 yards with an interception.
Marcus Sherels supplied the Vikings' only touchdown on an 86-yard punt return in the first quarter.