Prior and Broad buckled themselves into the crease at the start of the final session with the score 237 for seven, intent on batting the hosts out of the game. They batted together for 137 minutes.
England lost Broad for six with 21 balls left. The visitors finished on 315 for nine. New Zealand failed to take 20 wickets for a fifth consecutive test but there was no lack of heart trying to do so as Boult charged in over the final six balls.
Prior anchored England with his seventh test century, finishing on 110 not out. Broad completed 103 minutes without scoring, breaking Geoff Allott's 14-year-old record by two minutes.
In Everest parlance, New Zealand moved to their Hillary Step by tea. They required three more wickets with 32.3 overs remaining after Ian Bell was dismissed for 75.
England were stubborn and New Zealand were unrelenting. Attrition reigned. If it was a movie, a subliminal message would have kept popping up on the screen which reads: 'how good is test cricket?'
The bowlers McCullum had persevered with all series keep toiling. Most deliveries produce palpable reactions from a raucous crowd; the playing field had a magnifying glass on it.
The visitors required 481 to win, although that was irrelevant as McCullum employed attacking fields throughout.
Boult captured Joe Root lbw for 29 on the eve of lunch. It was the first delivery with the second new ball, following on from his career-best six for 68 in the first innings.
New Zealand lapsed when Boult had two catches dropped in the cordon by Dean Brownlie (fourth slip) and Williamson (gully) in the last over before lunch. Bell was 40 and Jonny Bairstow was two. Boult kicked the ground in despair when clipped into the legside next ball. Southee put a comforting arm around him as they exited the field.
A Southee ball to Jonny Bairstow deviated and had him caught by Taylor at first slip for six after lunch. Southee continued an outstanding spell with three further close calls. He had a decision for lbw reversed off Prior as well as a caught behind which never hit the bat.
Wagner narrowly missed catching a Prior pull in the air to deep mid-wicket. He also hit Prior at one point; the ball ballooned away and hit the base of the stumps but refused to dislodge a bail.