The tourists, chasing 190 for victory in Auckland on Saturday night, limped to 8-108.
The result was a big turnaround from the 203-run defeat the Black Caps suffered in the final one-dayer between the sides in Hamilton on Wednesday.
The West Indies couldn't repeat their batting performance, with Andre Fletcher's 23 their best score, while the home side tightened up their bowling.
Nathan McCullum celebrated his 50th appearance in a T20 with 4-24 and he was aided by some excellent catching.
Skipper Brendon McCullum, who contributed a half-century to New Zealand's 189-5, was delighted with his side's display.
Brendon McCullum was full of praise for Ronchi, who produced his highest T20 score of 48.
"It was a brilliant innings because it wasn't that easy to score," Brendon McCullum said of the 25-ball knock that overshadowing his captain's knock.
"He really gave us the impetus we needed at the back end of the innings."
Former Australia representative Ronchi hit seven boundaries, including four sixes, two of which came in a haul of 22 runs from one Sunil Narine over.
West Indies skipper Dwayne Bravo said chasing 190 was always going to be difficult and the regular loss of wickets increased the pressure.
He said the tourists were looking forward to the chance to turn the tables in the second and final T20 match in Wellington on Wednesday night and he had a light-hearted warning for his counterpart.
"It's always good to be with our backs to the wall," Bravo said.
"That's when we're the most dangerous, so Brendon, look out."