After restricting the Sixers to a modest 116-9 in their 20 overs courtesy of a miserly 3-17 by spinner Matthew Kuhnemann, the Heat battled their way to 117-6 with 10 deliveries to spare.
"We're a Queensland team and the great Queensland teams, when their backs are against the wall, they find a way to win. It's something we've tried to (grow) within our psyche," said Brisbane captain Jimmy Peirson.
With batsmen Usman Khawaja and Marnus Labuschagne in India with Australia's test squad, it was left to domestic player of the year Michael Neser (48 not out) to steer the run-chase after the Heat middle order collapsed and the side reeled at 56-5.
The knockout match remained in the balance until Neser released the pressure that had been building by peeling four successive boundaries off seamer Hayden Kerr in the 16th over.
The Heat now travel to Western Australia to face defending champions Perth Scorchers in Saturday's decider.
