The visitors trailed 26-7 at half-time but ran in four converted tries after the break to avoid the ignominy of posting the longest losing streak by a New Zealand Super Rugby team.
Damian McKenzie started at fullback but orchestrated the victory from the playmaker role and converted all five tries as the visitors beat the Hurricanes for the first time since 2018.
Centre Chase Tiatia sparked the comeback after coming off the bench to score a try in the 57th minute and then play a part in a brilliant move that led to another for halfback Brad Weber a minute later.
Lock Naitoa Ah Kuoi crossed off the back of a rolling maul eight minutes later to level up the score at 26-26, allowing McKenzie to give the Chiefs the lead with the conversion.
Jordie Barrett kicked a long-range penalty six minutes from time to edge the Hurricanes back in front but the Chiefs would not be denied and No.8 Luke Jacobson smashed his way over the line for the winning try a minute later.
"It would have been pretty easy to fold after the last 10 or so games and going three tries down," said Chiefs captain Sam Cane.
"But I'm proud of the way we stuck to our guns. We never gave up, we hung in there and battled our way back. Hopefully we can build on that."
The Hurricanes had looked set for the first win of the campaign at halftime after halfback Luke Campbell and hooker Ricky Riccitelli had crossed the line before two tries from winger Salesi Rayasi.