Replacement lock Justin Sangster scored the winning try two minutes from time to hand the dominant team in Super Rugby for most of the last three decades a fourth straight loss for the first time in their glorious history.
The wet conditions made for a scrappy contest and the return home for their first match on their own turf this season did nothing to turn around the fortunes of the winless reigning champions.
Prop Tyrel Lomax gave the Hurricanes the lead in the 14th minute but the Crusaders kept the visitors out for the remainder of the first half and levelled up the scores when No 8 Cullen Grace crashed over the line in the 54th minute.
First five-eighth Riley Hohepa put the Crusaders ahead with a penalty in the 71st minute but the Hurricanes besieged the try line and the home side, reduced to 14 men by a yellow card, finally cracked seven minutes later.
"It's a tough place to win," said Hurricanes replacement halfback TJ Perenara.
"Coming down here and playing the Crusaders outfit, I know they haven't started the season the way they wanted to, but they are always a force to be reckoned with and getting a win over them down here is important for us."
Crusaders captain for the match David Havili said the poor start to the season was not because of a lack of effort.
"It's just trusting our stuff," he said. "We can build phases, we can really punish teams, but at the moment we can't get over a certain amount of phases to do that.
"So it is frustrating at times but the boys are trying their guts out. Proud of the effort tonight but it's tough one to take."
After winning a Super Rugby title for the seventh straight season last year, the Crusaders lost coach Scott Robertson to the All Blacks and key players Richie Mo'unga and Sam Whitelock to lucrative contracts overseas.
New coach Rob Penney is also without All Blacks standout Will Jordan for the season and skipper Scott Barrett for six weeks because of injury.
"We're not using that as an excuse, it's next ones up," Havili added.
"We've got a young group that are willing to try, willing to turn up each day and get better. So that's all we can ask for, and that's what we're going to do."
