New York had not won a playoff game since capping the 2011 season with the franchise's fourth Super Bowl, but they rode a pair of strong performances from their offensive centrepieces to upset the 13-4 Vikings on the road.
Quarterback Daniel Jones became the first player to ever tally 300 passing yards, two passing touchdowns and 70 rushing yards in a playoff game, while star running back Saquon Barkley had 109 yards from scrimmage and scored two rushing touchdowns.
Incredibly, neither team committed a turnover, with Vikings quarterback Kirk Cousins also delivering an impressive 273 yards and two touchdowns, but he was unable to produce in the fourth quarter.
It was the Vikings who scored first through a Cousins quarterback sneak from the opening drive of the game, but their lead did not even last until quarter time as Barkley and receiver Isaiah Hodges found the endzone in response.
After trading scores in the second and third periods, the Vikings pulled things level at 24-24 early in the fourth with a field goal, but Jones answered with a defining 12-play, 75-yard drive, setting up Barkley for the game-winning touchdown.
The Vikings had two drives and seven minutes to try and tie things up, but the Giants' defense rose to the occasion and closed it out.
New York will try to continue their march to the Super Bowl next week in the Divisional round against the league-leading Philadelphia Eagles (14-3).