It left the three-match series tied at one win apiece, with the All Blacks taking the opener at Eden Park before the touring Lions leveled it with a narrow victory in Wellington last weekend.
The All Blacks led 15-12 with just three minutes left of a fiercely contested encounter until Owen Farrell kicked his fourth successful penalty to tie the scores.
Intense All Blacks pressure at the end came to nothing to leave an outcome which nobody had expected, only the second time in the 129-year history of the Lions that a series had ended all square and the first tie between the two sides.
All Blacks captain Kieran Read, who was making his 100th Test appearance, summed up the mood in the home camp as he reflected on the tied series.
"I feel pretty hollow. To walk away with a draw doesn't mean much," he told Sky Sports.
His Lions counterpart Sam Warburton agreed: It's better than losing I guess.
"I don't know what I made of that I was ready to go into extra-time," added the Welshman..
Warburton and the team coached by Warren Gatland were trying to match the achievement of the last Lions team to win a series in New Zealand in 1971.
They came up short, but always trailed in the decider until Farrell's nerveless kick backed up a superb second half performance by the Lions.
They had trailed 12-6 at halftime after the All Blacks capitalized on early domination with a fine try by Ngani Laumape, converted by Beauden Barrett.
Two penalties by Farrell narrowed the gap to just a point, but before the break Jordie Barrett went over for a second All Blacks try and it looked ominous for the visitors.
But the Lions gained early heart after the break when Elliot Daly converted a penalty from within his own half to cut the gap to three points.
The home side's Jerome Kaino was sin binned just before the hour mark and while he was off the field Farrell's third successful penalty drew his side level for the first time.
Beauden Barrett edged the All Blacks ahead again with his first successful penalty before Farrell set up a dramatic finale.
From the kick off, the All Blacks were originally awarded a penalty by referee Romain Poite as Ken Owens was blown for offside after the ball bounced off teammate Liam Williams and forward into the hooker.
But after the video referee reviewed the decision it was downgraded to an All Blacks scrum, from which they failed to take advantage.
"I thought it would have been harsh for either side to lose," said Warburton.
"We showed some real courage," added Kiwi Gatland, who had come in for ferocious pressure from the New Zealand media as his side struggled in the early matches and fell 1-0 down in the series.
New Zealand coach Steve Hansen could not mask his disappointment after his world champion side came so close to winning a series where they had started as firm favorites.
"It's come down to the wire and we've ended up with one hand on the trophy each which is a bit like kissing your sister," he reflected.
The draw also ended a 38-match winning streak for the All Blacks at Eden Park, dating back to 1994.
"But it's been a wonderful advertisement for rugby," added Hansen.