Prior scored an unbeaten 110, and held firm alongside last man Monty Panesar, as England closed on 315-9.
“I’m not one to celebrate draws but to escape with that is a phenomenal effort,” said Prior.
“I think Monty had been sleeping so I had to wake him up first, but he was magnificent. I knew he’d be fine.”
Prior revealed that he invoked the spirit of Cardiff 2009, when Panesar defied Australia alongside James Anderson in a game-saving last wicket stand.
“He was actually really calm,” said Prior, after the duo batted out the final 19 balls under intense pressure at Eden Park. “We mentioned the Ashes, we mentioned Cardiff. He was really chilled out.”
“My role is to help him with game plans, tell him this is what they’re going to do, this is how they’re going to try to get you out.”
“All our guys have been working so hard in the nets for that exact moment.”
Earlier in the day Ian Bell and Joe Root had set the tone by batting out almost the entire first session, before losing the latter to the first ball of the new ball.
Bell scored a resolute 75 from 271 balls, but his departure on the stroke of tea left Prior to steer the tail-end batsmen through to the close.
The wicketkeeper praised Stuart Broad, who took a record 103 minutes to score a run for a 77-ball innings of six runs.
“The way Joe Root and Ian Bell started this morning was phenomenal and I have to give a special mention to Stuart Broad,” said Prior.
“The way Broady played was phenomenal. He’s been working so hard with Andy Flower in the nets and has been getting frustrated with it.”
“Forget what score he got, the amount of balls and the amount of time he took out of the game was phenomenal.”
Prior’s 185-ball 110 from four hours and 29 minutes at the crease was the longest innings of his Test career, which has now included seven centuries.
Asked how he approached the day, Prior said: “You’ve got to find a way to face 90 overs. The wicket was still good, and we knew it was only going to get slower. You just dig in for as long as you can.”