Wales tore into their visitors from the start. Tomos Williams, one of the players Wales are building the team around, scored within 90 seconds. Wales scored a second try a few minutes later.
Cardiff stirred, but Wales know an early score against New Zealand has often meant little on its own.
Wales sent another penalty to touch with time up at the end of the first half. There was a sense then, as there was at half-time, that the match could slip away.
Wales kept coming. They used precision and power against a much-changed New Zealand team, taking advantage of misconnections in the visitors' play. They scored twice more within 10 minutes of the restart.
The loudest noise in the last quarter greeted defence, not a run of further scores. The roars were such that a passerby might have thought Wales had crossed the line time after time.
New Zealand will still claim top spot in the southern table of the championship, but on two bonus points rather than the five-pointer that had been expected.