Both sides went into the match in poor form but it was the winless 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 regain 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.