Hobart will chase 163 for their first Big Bash League road victory this season and a spot in the top five.
Sent in by Matthew Wade, Brisbane were circumspect against some tight bowling and hit only a solitary six in the innings.
But, helped by 11 Hurricanes wides, they scrambled to 6-162 in the hunt for a third-straight win.
The winner of Friday's clash with jump the stalling Adelaide into fifth and take ownership of a finals spot with two games to play.
Joel Paris, in for the injured Paddy Dooley, took 2-15 bowling with the new ball and at the death.
Brisbane's last-game hero Matthew Renshaw (41 off 31) upped the ante in the 14th over, finding the rope three times off Riley Meredith.
But the big quick stuck to his guns and had the in-form left-hander well caught by Nathan Ellis in a major setback for the hosts.
Faheem Ashraf's next over went for just three to ensure any Heat momentum was lost.
English import Sam Hain, raised on the Gold Coast, was unbeaten on 33 off 25 and James Bazley scored a crucial 13 off six balls.
Meredith (2-42) bowled Josh Brown for a duck in the first over then grabbed Renshaw's wicket but, a victim of the power surge, was taken for 30 runs from his final two overs.
Usman Khawaja (18 off 17) tried to spark the innings but was cleverly dismissed by Faheem.
A slower ball with his first delivery of the innings drew a false shot from the Test opener and a sharp caught-and-bowled from the Pakistan import
The Hurricanes are confident Dooley (groin) will return for their final two regular season games.
