New Zealand, who hold a 1-0 lead after a comprehensive victory in Wellington last week, have not beaten a top-eight nation in a series since they beat West Indies 2-0 in 2006.
The hosts had resumed on 6-0 with Peter Fulton on four and Rutherford yet to score and after some nervous moments against Darren Sammy and off-spinner Sunil Narine still managed to push the score along to 33-0 at an impressive rate.
Fulton, however, became the fourth victim of Sammy's brilliance in the field, hammering the ball back at the West Indies captain who nonchalantly took a caught and bowled opportunity to dismiss the tall opener for 10.
Rutherford had become bogged down against Narine after Fulton's dismissal but broke the shackles when he cut the ball between point and cover-point in a packed off-side field to the boundary on the last delivery before drinks.
New Zealand's pace bowlers had set up the small victory target late on Saturday when they destroyed West Indies' second innings by capturing all 10 wickets in the evening session.
Trent Boult had blown the top off the order before Tim Southee polished off the tail to pick up his 100th test wicket as New Zealand dismissed the tourists shortly before the close for just 103 runs.
(Reporting by Greg Stutchbury in Wellington; Editing by Ian Ransom)
