And, coincidentally, it was against the Kiwis in Auckland that it all began for Hines after he was flown out to the tour just six days earlier as an injury replacement.
Now, 64 caps on, the fire still burn just as brightly, although Hines admitted: "Chris Paterson also played in my debut and I was saying to him just the other day 'think of the oldest guy you played rugby with when you were young and imagine how old he is now'. We agreed it was a scary thought!"
On current form Hines still has much to give especially as he has just been hailed by ex-coach Jim Telfer as the "master off-loader" in tribute to his ability to pass out of tackles.
Though reluctant to look too far ahead it is clear, too, a third World Cup, due to be held in New Zealand next year, is on the radar of this 33-year-old Leinster-based second row who was born in Australia and owes his Scots allegiance to a grandparent from Govan.
"It's a cliche but the match on Saturday week is the start of the World Cup build up. Between now and then it will be about putting consistent performances together."
In one respect Scotland have been a model of consistency against New Zealand - they haven't beaten them in 27 meetings - so what are the prospects of a change of fortune?
Hines was part of the Scotland squad that defeated Australia at Murrayfield last Autumn and he believes that result had a profound effect on morale.
He said: "It showed top Southern Hemisphere sides could be beaten by us but we will have to go up a level against New Zealand.
"We will put as much pressure on as we can and if things are done right it could happen for us.
"Ask any athlete and they'll tell you that measuring yourself against the best in the world is what it is all about.
"And, believe me, New Zealand are best by a long way.
"We'll draw on that but things are going to be even harder because New Zealand have just been beaten by Australia in Hong Kong on their way across and come this part of the tour (it starts against England at Twickenham on Saturday) there will be no lack of motivation for them.
"Losing to Australia is nothing to be ashamed of, especially in a match of exceptional standard and high intensity.
"Nevertheless, England will be in for a tough time and New Zealand will want to go through the rest of their tour unbeaten even more.
v NEW ZEALAND
Saturday, Nov 13, 5.15pm
v SOUTH AFRICA
Saturday, Nov 20, 2.30pm
Saturday, Nov 27, 2.30pm (Pittodrie) There is going to be a backlash from them."
New Zealand were thwarted by the Wallabies just two short of setting a new world record winning sequence, and the Scots are building a bit of momentum themselves.
A draw with England was followed by victory in Dublin and a two-match Test series triumph in Argentina.
Injury cost Hines his place against Ireland and the death of his mother-in-law from a brain tumour saw him fly off to Australia at the end of the domestic season to be with his wife, Leanne, instead of joining the squad in South America.
"Rugby is important to me and going to Argentina would have been good but other things are important, too.
"Despite missing the Argentina tour I know the lads have had one eye on playing the All Blacks ever since.
"They are playing the type of rugby we want to play and the benchmark has now been set much higher.
"Finishing last season on a four-match unbeaten run was certainly a confidence booster and we know we are going in the right direction.
"It's a shot-in-the-arm alright to know that hard work is paying off and hopefully that will lead to crowds being behind us the way they were when Australia were beaten last Autumn.
"But success in the past is no guarantee of success in the future," he added.
Meanwhile, Hines was praised by national coach Andy Robinson as a three-day training camp at St Andrews ended.
"Nathan, in the last couple of weeks, has been superb," said Robinson and, ironically, his last fine performance was at the expense of Edinburgh in the Magners League.
However, Hines missed the earlier fixture at Murrayfield and he revealed the bizarre circumstances of his absence.
"I got a toe stuck in the couch at home and as I rolled on to the floor I heard a crack.
"My wife examined the damage after she'd stopped laughing and told me the toe was broken. The Leinster medics agreed and that was me out for a game."
Now fully recovered Hines is only too willing to put his best foot forward if, as seems likely, he faces the All Blacks for the third time in his Scotland career next week."
"It is the start of the World Cup build up. It will be about consistent performances" nathan hines