He came out after drinks with a six down the ground in the 19th over but his desire to repeat the dose eventually brought his downfall.
Fulton and Williamson then steadied proceedings after the loss of Rutherford and will look to build on their promising beginning as the day wears on.
New Zealand have taken a forward-thinking approach in to the test with the selection of promising leg-spinner Ish Sodhi and all-rounder Corey Anderson to make their first test appearances.
The Black Caps - like most international sides - have longed for a leg-spinner of decent quality for many years and while it would be premature to suggest Sodhi is the future, the 20-year-old has clearly impressed the right people in a short space of time.
He has only played 14 first-class matches and a handful of limited-overs fixtures for Northern Districts and the national A side.
The Indian-born tweaker will get ample opportunity to press his case for further selection as the test match progresses given the low-and-slow nature of the wicket in Chittagong.
Anderson, meanwhile, has won his way in to test cricket on the back of a century for New Zealand A on their tour of India last month.
The 22-year-old has long been classed as an international-cricketer-in-waiting after he was first contracted by Canterbury as a teenager but he's taken a while to fulfil his lofty potential.
Given he bats and bowls left-handed, Anderson offers a key point of difference for New Zealand and gives them a genuine option as an all-rounder, which like their search for a leg-spinner, has been another position that has proved challenging to fill in recent seasons.
Bangladesh also named a debutant with the selection of top-order batsman Marshall Ayub. The 24-year-old boasts a competent first-class record with seven centuries at an average just under 37 and has been picked in the absence of Mohammad Ashraful.
Ayub will likely get a chance to impress on day two or three as the New Zealanders look set for a long stay at the crease in their first innings.
