Eli Manning's side went into the match with an 0-6 record, while Minnesota had also made a poor start to the campaign with one win from five games.
Both sides showed a lack of confidence in a slow start at MetLife Stadium but it was the Giants who broke the deadlock, just after Hakeem Nicks had dropped a Manning pass in the end zone.
Josh Brown picked up the pieces to convert a 35-yard field goal, but Minnesota responded in style to score the opening touchdown late in the first quarter.
Marcus Sherels was the man who produced an inspired solo run for the Vikings, breaking several tackles to find the end zone on an 86-yard punt return.
The Giants used that initiative to take the lead as Manning found his range, picking out Rueben Randle with a 24-yard touchdown pass into the corner.
Vikings kicker Blair Walsh missed a chance to level with a field goal soon after, with the Giants holding firm to maintain their slender advantage at the break.
After the break New York took complete control of the clash with their second touchdown after Sherels blotted his copybook by gifting New York possession five yards from the line with a fumble.
Peyton Hillis took full advantage with a sharp score, while Freemnan's woes continued for the Vikings as their attempts to mount a response floundered.
Two Brown field goals inched New York out of sight in the fourth quarter, ending a six-game losing streak as Manning threw for more than 200 yards.