Sherfane Rutherford hit a sublime unbeaten 68 as West Indies fought back to beat New Zealand by 13 runs to book their place in the T20 World Cup Super 8s.The co-hosts were in trouble at 22-4 when Rutherford came to the crease and continued to struggle for much of the innings, slumping to 30-5 and 76-7. But Rutherford kept his cool and timed his onslaught to perfection as he took 37 from the last two overs of the innings to lift West Indies to 149-9 in Trinidad.That proved to be more than enough on a two-paced surface as New Zealand fell away in the middle overs of the chase.Fast bowler Alzarri Joseph took 4-19 and left-arm spinner Gudakesh Motie 3-25 as the Black Caps, after some late hitting from Glenn Phillips and Mitchell Santner, ended on 136-9.While the Windies can look forward to the next stage of a home tournament, back-to-back defeats leave New Zealand’s qualification hopes hanging by a thread. They must now beat Uganda and Papua New Guinea in their remaining games and hope other results go their way.They could be eliminated before they play again if Afghanistan beat Papua New Guinea on Friday.Prior to the match, the atmosphere at the Brian Lara Academy was one of excitement and anticipation after two victories to start the tournament for the home side.