Thrashed in their opening match by Afghanistan in Guyana and therefore in a virtual must-win situation, the Black Caps never developed any momentum in the chase in being restricted to 136 for nine.
Pacer Alzarri Joseph (4 for 19) and spinners Gudakesh Motie (3 for 25) and Akeal Hosein (1 for 21) kept the home side in control to clinch their third consecutive victory and a place in the Super Eight phase of the competition with one group match still to come against Afghanistan on Monday in St Lucia.
Only Glenn Phillips (40 off 33 balls) caused any real worries for the West Indies but when he fell to Joseph in the 18th over the match was effectively over as a contest, despite Mitchell Santner belting three sixes off Romario Shepherd in the final over.
This second consecutive setback effectively ends New Zealand's hopes of advancing out of the group stage, unless other results can contrive to work in their favour. The Kiwis will be eliminated if Afghanistan defeat Papua New Guinea on Thursday.
"Keeping it simple and backing my skills, I think that was the key," said Rutherford in explaining his formula for success on the night after receiving the "Man of the Match" award.
'Play a blinder'
"Looking at their bowling line-up I knew they were short two overs and I told myself to just be there at the end to make the most of it...and I thought I did that."
Rutherford received invaluable support from the lower order, adding 28 with Akeal Hosein for the sixth wicket, 27 with Romario Shepherd for the eighth and then plundered all 37 runs in the last two overs of the innings, bowled by Daryl Mitchell and Santner, with last man Motie happy to look on from the non-striker's end.
Earlier, Trent Boult led New Zealand's much-improved, finishing with the excellent figures of three for 16. Lockie Ferguson and the recalled Tim Southee complemented that effort with two wickets each as the 2021 beaten finalists looked much sharper in the field than against the Afghans.
"We knew it was going to be difficult to get runs on this wicket which is why the quality of Sherfane's innings was of the highest," acknowledged losing captain Williamson.
"We took a decision to try to bowl them out, but unfortunately it didn't come up for us today."
After victories over Papua New Guinea and Uganda at the Guyana National Stadium, West Indies' batting seemed unprepared for the challenge, until Rutherford intervened to transform what was shaping up as an abject capitulation.
"It is good that, after finding ourselves in so much trouble early on, the guys dug deep and we were able to pull this one out," said West Indies captain Rovman Powell.
"From the hotel the message was that someone would have to play a blinder. We always believe that individual brilliance is needed sometime in T20 cricket and Sherfane's knock was a fantastic effort. It gave us confidence and at the halfway mark we believed (we could do it.)