Wes Goosen and Vaea Fifita crossed during the man advantage for the home side, who had been 23-7 down at halftime and trailing 31-17 with 13 minutes remaining.
"It's very frustrating, they are the Super Rugby champions and a very good side," said Lions captain Rory Best.
"We'll look back at mistakes that let them back into it. But to build two leads the way we did at this stage in the tour, we've got to look at a few positives as well.
"You cannot fault the effort but we needed to be maybe a little more clinical at times."
The Lions had spent much of the first half defending but managed two opportunistic tries with winger Tommy Seymour finishing off a length of the field movement after Greig Laidlaw had made an intercept with the Hurricanes hot on attack.
George North also scored after the home side failed to field a high kick from flyhalf Dan Biggar and the ball bounced kindly for the Lions right winger, who crossed under the posts.
The Hurricanes did not help themselves as they turned the ball over just when they appeared to be getting momentum or gave away silly penalties inside their own half, allowing Biggar to knock three over to give his side a 23-7 lead at the break.
The home side struck back almost immediately after the resumption of play with Laumape finishing off a well-worked backline move that ended with the All Blacks squad member smashing over the top of Biggar.
Jordie Barrett and Biggar traded penalties before Seymour grabbed his second try with scrumhalf Te Toiroa-Tahuriorangi yellow carded for a high tackle as the visitors built their 14-point advantage.
Henderson, who had been outstanding in the second half, was then given a yellow card for a dangerous tackle on Jordie Barrett, allowing Goosen to cross before Fifita smashed over following a sustained buildup.
Biggar had the opportunity to win the game with a long range drop goal attempt after the fulltime hooter but it fell well short.
"We wanted to put on a performance today and it's frustrating because I think we gave away a few soft penalties early," said Hurricanes captain Brad Shields.
"But look, a massive game and an awesome occasion and I think the boys loved every minute of it. And the fight out there to come back in that second half was unreal and just great to be a part of."
(Editing by Sudipto Ganguly)
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