It also marked a satisfying start to his test captaincy reign for Kane Williamson.
He paid tribute to the work of his bowlers in Zimbabwe's first innings when they were bowled out for 164.
''For us that first innings bowling, after losing the toss on a good surface, was outstanding by our boys and which certainly put us ahead of the game," he said.
The day began with Zimbabwe in a hopeless position, and things deteriorated in the second over of the morning when they were victims of another poor umpiring decision.
Craig Ervine has just completed his first test 50 when he was given out caught behind off left armer Trent Boult. Replays showed a clear gap between bat and ball but there is no DRS system in use in the series.
Williams had been off the field for the second and third days with illness but the lefthander immediately embarked on a shot-playing mission.
He drove expertly but also made use of a good sweep shot, clever ramp shot and although he chanced his arm occasionally it was a hugely impressive innings.
At lunch, Zimbabwe would have been pleased to have dominated a session for the first time in the match, as it had been one-way traffic through the first nine sessions.
In the first innings, Sean Williams had been given out when the ball clearly bounced straight onto his helmet into the hands of a fielder.
He made up for it second time round, getting to his century in 106 balls, the fastest ever by a Zimbabwe centurymaker.
At one point he took four boundaries in 11 deliveries by Tim Southee. Legspinner Ish Sodhi came in for some treatment, although also coming close to beating Williams with one delivery.
He finally holed out to deep midwicket off left arm spinner Mitchell Santner, who bowled tidily. Williams batted 205 minutes in an entertaining, skillful and gutsy innings.
Cremer grafted away, happy to take the odd blow on his body in scrapping his way to 33 before being adjudged lbw to Sodhi. On other days the ball might have been judged to have gone over the top of the stumps.
Boult finished with four for 52, but Neil Wagner took the final wicket to finish with eight for the match.
Zimbabwe captain Cremer acknowledged that having been 20 months since their last test, it was a difficult assignment for his team.
''I suppose it is tough for us, but we didn't learn after that first innings against the new ball," he said.
''I thought we were a bit soft. Hopefully in the second test we will be a lot more prepared for that."
The man of the match award went to New Zealand batsman Ross Taylor for his unbeaten 173.
The second test starts on the same ground next Saturday.
