New Zealand are on the brink of elimination at the group stage of the men’s T20 World Cup after falling 13 runs short of West Indies’ target at the Brian Lara Academy in Trinidad.

The co-hosts recovered from a horror start in Tarouba as Sherfane Rutherford came to the rescue, his unbeaten 68 helping to build a total of 149 for nine that proved enough for victory on Wednesday.

West Indies restricted New Zealand to 136 for nine in reply, with Alzarri Joseph claiming four wickets and Gudakesh Motie three, sealing a third consecutive win and a spot in the Super Eights.

New Zealand have lost both their matches and now need to defeat Uganda and Papua New Guinea and hope other results go their way to leapfrog Afghanistan and snatch a spot in the next phase.

The Black Caps were on top early as their fast bowlers took four wickets in the powerplay and Jimmy Neesham added another to have West Indies reeling at 30 for five. Rutherford then led the fightback in stands with Akeal Hosein, who scored 15, Andre Russell (14) and Romario Shepherd (13), before playing a lone hand in the dying stages.

West Indies were nine down for 112 when Joseph was bowled by Trent Boult with the fifth ball of the 18th over, but Rutherford took charge in the last two overs, blasting 37 crucial runs. The left-hander reached his highest T20 international score with a boundary off the last ball, reaching 68 not out off 39 balls including six sixes and two fours.

“It was a good innings,” Rutherford said. “Playing a World Cup match is a dream, that is what we live for. I’m just happy to contribute.

“It was a very tough surface to bat on. My plan was to bat deep, I was telling the bowlers that even if we just get singles, it all adds up. 149 is a brilliant score on this wicket.”

New Zealand made a bright start to their chase as Finn Allen (26) went after the West Indies’ attack. But once fellow opener Devon Conway (five) was the first to go with the score on 20, the Black Caps’ middle order was unable to build another significant partnership as they slumped to 85 for six in the 16th over.

Glenn Phillips (40) helped keep New Zealand’s hopes alive but once the all-rounder fell with 41 runs still to get from 14 deliveries the result was all but assured. A late cameo from Mitch Santner with three sixes in his 21 not out lifted New Zealand to 136.

“The quality of Sherfane’s innings was high,” the New Zealand captain, Kane Williamson, said. “The batting depth in their side was beneficial for sure.

“We cannot make excuses, we just need to bounce back quickly. We are back on in a couple of days and we want to see better and smarter ­performances. The effort was there, and it’s important that we pick ­ourselves up and go again.”

Afghanistan will join West Indies in progressing from group C to the Super Eights if they beat Papua New Guinea on Thursday night local time. New Zealand face Uganda the following night but their campaign may be over by then, potentially ending a streak of reaching the semi-finals at the past three men’s T20 World Cups.