A break in the rain marked a turnaround for the Hurricanes, who put heat on the Chiefs inside their half for the next 15 minutes. The visitors turned down two opportunities to kick for goal and were rewarded with a try to Jack Lam which was converted by Barrett, reducing the Chiefs' lead to 16-13.
Rennie would have been pleased with his forwards' hustle in the second half as they out-muscled their opposites at the breakdown.
Hungry for the win, the Chiefs chose to kick for goal instead of running the ball with 15 minutes remaining. Cruden took the lead out to 19-13.
But the Hurricanes replied shortly after, rumbling it up the middle for replacement prop Tristan Moran to go over. Barrett's conversion put them ahead, for the first time, 20-19.
They were soon back on the Chiefs line, Barrett's penalty making it 23-19 after defenders strayed offside.
With time up, the Chiefs had a last chance to win the match when they had a 5m scrum. They blew it and the Hurricanes cleared to end the match.
23 Hurricanes
Tries: J Lam, T Moran; pens: B Barrett 3;
cons: Barrett 2.
19 Chiefs
Try: B Leonard;
pens: A Cruden 4;
con: Cruden.
HT: 6-9.