Scotland’s Mark Bennett, Wales’ James Davies and Englishman Dan Norton all crossed in a stunning first-half onslaught to race into a 21-0 lead and leave the Kiwis reeling.
New Zealand were already licking their wounds after being shocked 14-12 by Japan and losing superstar Sonny Bill Williams to injury in their opener yesterday. The defeat to Britain left them out of the top two in Pool C but they squeezed into the quarters as one of the best third-placed sides.
New Zealand hit back in the second half and scored three tries of their own but one missed conversion proved the difference.
Japan took second place as they beat Kenya 31-7.
GB will now face Argentina in the last eight at 10pm.