After winning the toss and putting New Zealand in to bat on a green-tinged Dunedin wicket with heavy cloud overhead, West Indies skipper Darren Sammy had reason to feel luck was on his side.
But that was one of the few things to go the West Indies' way as they struggled to contain the free-scoring New Zealand batsmen.
At tea, Ross Taylor was unbeaten on 39 with Brendon McCullum on six. Rutherford was out for 62 and Fulton for 61.
Rutherford was dismissed shortly before lunch after a brisk 95-run partnership with Fulton as the West Indies quicks were unable to generate much movement despite the conditions.
Rutherford's innings included a six and 10 boundaries but he came undone when taking the long-handle to Shane Shillingford.
After dispatching Shillingford for a six and a four, his attempt to hit the spinner out of the ground saw him caught one-handed on the boundary by a leaping Narsingh Deonarine.
Aaron Redmond, back in the side after a five-year absence, kept the momentum going after lunch until he miscued an attempt to turn Tino Best down the leg side and sent a leading edge to Marlon Samuels in the gully.
Best, bowling with more control after lunch, was unlucky not to be rewarded with a second wicket when he rapped Ross Taylor on the gloves early in his innings only to see the ball sail over the slips cordon and race to the boundary for four.
Fulton moved sedately to 38 before unleashing three quick fours for his half-century.
But when he reached 61, a lapse of concentration saw him jab at a Sammy delivery and Kirk Edwards took a regulation catch at second slip.
Shillingford was the pick of the West Indies bowlers, with one for 31 off 15 overs.