A double-century in a one-day international is not quite passé, but has become more common than ever seemed possible. A double-century in a World Cup quarter-final? That is something truly special. Martin Guptill's unbeaten 237 was the highest World Cup score of all time and the second-highest in all ODIs, but most importantly it ensured New Zealand's progression to the World Cup semi-finals for the seventh time.

Nobody in the partisan crowd in Wellington will ever forget Guptill's innings. Nor will Marlon Samuels, who in the first over of the match grassed Guptill at square leg. It is hard to imagine a costlier one-day drop, for Guptill went on to score 60% of New Zealand's 393 for 6. To add to the hurt, Samuels later fell to the most brilliant of catches, when a backpedalling Daniel Vettori at third man leapt and pinched a one-hander above his head that would have gone for six.

It was that sort of day for New Zealand. Buoyed by the home support, they did just about everything right. West Indies kept up with the run-rate, just not the preservation rate required. They limped past Guptill's individual tally at nine wickets down, and were bowled out for 250 in the 31st over. Trent Boult had done the damage by claiming four wickets in his opening spell.

Chris Gayle pummelled 61 off 33 balls and provided some evening entertainment. Stiff with a bad back, Gayle dealt almost exclusively in boundaries. He struck eight sixes and two fours, and his innings was the most one-sided thing in a one-sided game: only one of his runs came through off. But he was bowled by Adam Milne for what was but a cameo compared to Guptill.

Guptill had faced the first ball of New Zealand's innings and the last. He played proper cricket shots, premeditating little but punishing the West Indies bowlers when they offered up half-volleys. He saw off 65 dot balls, respecting the good ones and making the most of the others. He brought up his 200 with a powerful crunch down the ground for four off Andre Russell from his 152nd delivery.

It was fitting, for throughout his innings Guptill's straight driving was so impressive you'd think he'd just had a wheel alignment. Guptill basked in the standing ovation, knowing that this was a once-in-a-lifetime moment. When he had moved past 171, he had the highest World Cup score by a New Zealander, beating Glenn Turner's effort in their very first World Cup match back in 1975.

Guptill's 163-ball innings featured 24 fours and 11 sixes, and he alone scored 92 of New Zealand's 153 in the final ten overs. In the 50th over he even launched a six onto the roof. New Zealand knew they had the ingredients for a show-stopping product: a huge home crowd, a good pitch, a toss won, a shaky opposition attack. But Guptill cooked up something that spilled out of the Cake Tin entirely.

He scored freely throughout his innings but not surprisingly the flow of runs became an inexorable current during the late stages. His first half-century came off 64 balls and his hundred from 111. Do the maths and you'll realise that means his second hundred came from 41 deliveries. Wherever West Indies pitched it in the final ten over, Guptill had a six waiting for them.

This was a man at the peak of his powers: his 105 against Bangladesh in the previous game was just a warm-up. And though he scored 195 more than his nearest team-mate, he had plenty of support. The most prolific partnership was his 143-run stand with Ross Taylor for the third wicket; Taylor scored only 42 of those runs as he nudged the ball around for ones and twos.

In fact, the run out of Taylor arguably came at the perfect time for New Zealand, as it allowed Corey Anderson and then Grant Elliott to come in and find the boundary. Elliott's 27 off 11 balls was a fine cameo and his half-century partnership with Guptill came from only 15 legal balls. Jerome Taylor got rid of Elliott and Luke Ronchi at the end, but Elliott and Ronchi were not the problem.

The West Indian effort in the field was listless. Samuels' dropped chance was the stand-out, but the first ball of the game was ominous: Jason Holder and Sulieman Benn both lethargically pursued Guptill's straight drive. They could have saved the boundary, but didn't. West Indies became more disheartened as the innings wore on, and more mistakes were made.

Really, they'd have needed to do everything right after losing the toss. The first wicket was encouraging, as Holder lived up to his name by running away with the flight from mid-off and clinging on to a super catch to get rid of Brendon McCullum for 12. New Zealand were 27 for 1, but from there not much went West Indies' way.

Guptill and Kane Williamson put on 62 for the second wicket before Williamson drove Russell's slower ball to a juggling Gayle at cover for 33. But as long as Guptill was there West Indies - and a whole bunch of ODI and World Cup records - were anything but safe.

The result means New Zealand will host South Africa at Eden Park on Tuesday, a meeting that guarantees a first-time finalist at this World Cup. New Zealand have reached semi-finals at six previous World Cups but have yet to emerge from one victorious. In form and at home, they may never have a better chance.