The Lions could have closed the gap before the break when what looked like a perfectly fair try by Gareth Raynor – who touched down a grubber kick from Paul Wellens – was disallowed because of a dubious knock on decision from the video referee.
Less than a moment later Nigel Vagana took advantage of Great Britain’s defensive frailties to squeeze over the line, Stacey Jones converting, before the scrum-half combined superbly with Ruben Wiki to send Brent Webb over for the second.
At 10-0 it looked bleak for the tourists, but they gained a glimmer of hope when Danny McGuire’s cross-field kick was spilled by Manu Vatuvai with Gareth Ellis swooping onto the loose ball and touching down.
However the Kiwis responded when Jones sent Webb over for another try, and they were unlucky not to extend the lead when Frank Pritchard lost the ball at the corner.
Great Britain need to win here to be sure of a place in the tournament final, but it will need a great deal of work if they are to turn things around in the second half.