Brent Webb's try put the Kiwis ahead at half-time but Danny McGuire came close to putting the Lions back in the match.
As he went over the line, the ball looked to be punched from his grasp by Webb but no penalty try was given.
Motu Tony and Iosia Soliola added tries for the Kiwis before Paul Wellens and Gareth Ellis narrowed the gap late on.
Adrian Morley served notice to New Zealand in the opening minutes when he was put on report after thundering high into Kiwi skipper Ruben Wiki.
Sean Long was first to trouble the scorers on 13 minutes, kicking a penalty after Jerome Ropati flopped onto a completed tackle, but that was the only kick at goal either side had in the first half.
Try-scoring chances were also thin on the ground, and the only one that was converted in an evenly-fought first half came on 27 minutes.
With Great Britain bearing down on the goalline, Martin Gleeson kicked the ball through only for it to be gathered by Webb, who brushed off Brian Carney's challenge to sprint almost the whole length of the field and score.
The visitors ended the first half on the attack and continued after the restart, climaxing in a dancing move by Leon Pryce to set up McGuire to go over under the posts.
As McGuire crossed the line, Webb seemed to knock the ball out of his hands, but the video referee ruled against Great Britain.
Within minutes, the home side increased their advantage when Tony burst over the line under the posts to round off a neat close-passing move.
Morley, already on report, was lucky to stay on the pitch after clearly punching Webb before Soliola powered over the line to stretch the lead still further.
McGuire's beautifully angled kick-through set up Wellens to score as the visitors raised their game in the dying moments, and Long's chip forward set up Ellis to score right on the final whistle.
But time was not on their side and they were left to rue what might have been.
Report courtesy of BBC Sport.