Substitute forward Wallace Sititi sealed the 22-17 'Super Point' victory in Hamilton on Saturday night by scoring a try four minutes into the additional period after the scores were level 17-17 at fulltime.
A drop goal attempt to win the match from McKenzie was partially charged down before being grabbed by All Blacks back-rower Sititi, who powered across.
McKenzie was thrilled his side never wavered in the tense table-topping match after trailing 12-3 at halftime and 17-10 entering the closing stages.
"The Hurricanes have obviously been the benchmark all year and we knew we were going to have to be at our best and I just loved the fight from our boys," the New Zealand Test playmaker said.
"To stay in it, defend our line and then to be able to seal that one with Wallace at the end is awesome.
"The way the game unfolded, the moments that swung against us I'm proud of how we responded."
The result ended the Hurricanes' five-match winning streak and leaves them second, one point behind the Chiefs but with a game in hand.
Hurricanes coach Clark Laidlaw was impressed by how his team had the physical advantage for much of a defence-oriented match but felt they lacked composure in the closing stages.
"This was two teams filled with quality players have played internationally or or many, many games of Super Rugby," Laidlaw said.
"There's plenty to like there. But when you get 17-10 up away from home, you feel like you've got enough to close the game out.
"There's a wee bit of frustration there I guess."