The Crusaders were on course for their first win of the season when they led 28-22 with seven minutes left, but wing Alapata Leiua intercepted a loose pass to score a second try for the home side following Julian Savea's brutish earlier score.
Fly-half Beauden Barrett converted from in front of the posts to put his side ahead and complete a personal haul of 19 points against the record seven-time champions, who scored four tries but also gave away a string of careless penalties.
All Black fly-half Dan Carter had a chance to win it for the Crusaders but sliced his drop goal attempt wide of the left upright.
"That one could have gone either way," Hurricanes captain Conrad Smith said.
"They'll probably be disappointed in the way it slippedaway but we've had a few of those. We just wanted to hang in there."
The Hurricanes lost 34-20 to the Auckland Blues in their opening match before being edged 18-12 by the Queensland Reds last week.
The Crusaders remain without a win, although they collected the consolation of a losing bonus point and another for the tries from Ryan Cotty, Corey Flynn, Israel Dagg and Carter, who converted all four.
"We probably did enough at the start of the second half but we let them back in it," Crusaders number eight Kieran Read. said. "They're a good enough side to capitalise on our mistakes."
The opening try owed everything to the individual brilliance of Cotty, who beat four men to touch down. The inside centre dropped his shoulder to sneak between two players in the defensive line, shrugged off an attempted tackle from Tim Bateman and made it across the line despite being caught by Leiua.
Carter's conversion made it 7-3 but handling errors robbed the Crusaders of more points. Those errors proved crucial when Barrett knocked over three penalties to give the Hurricanes a 12-7 halftime lead.
The Crusaders were back in front, though, when hooker Flynn went over from close range and Dagg outpaced the chasing defenders for a try following his hack downfield from a soft turnover.
But Savea struck back with a try of sheer brute force, bursting through a challenge by Tom Marshall and repelling Dagg with such ferocity that the tackling fullback bounced backward off him.
Carter's converted try made it 28-19 but Barrett reduced the deficit with a 46-metre penalty and Leiua got his team to within a point, leaving Barrett to win it with the conversion.