The Heat started the day on 10 points with two games to play but vaulted into the top five with a 71-run victory clinched with 14 balls to spare at the MCG.
AB de Villiers laid the platform for the Heat with a searing 71 off just 37 balls, helping Brisbane to 186-5.
The table-topping Stars promptly collapsed in response, spinners Mitchell Swepson and Mujeeb Ur Rahman doing the damage for Brisbane as Melbourne were bowled out for 115.
DEVASTATING DE VILLIERS
Veteran De Villiers had not scored a half-century in the BBL going into Saturday’s contest, but he changed that fact in emphatic fashion.
The South African cleared the rope six times, with two of his sixes coming in an expensive Clint Hinchcliffe over.
De Villiers’ primary support came from Australia international Marnus Labuschagne, who finished unbeaten on a 13-ball 24, the pair combining for a fifth-wicket stand of 70.
STARS PUT IN A SPIN
Marcus Stoinis (17) got the Stars’ chase off to a strong start but it proved the first of two false dawns for the Stars, who lost Stoinis and Seb Gotch to James Pattinson in the fourth over.
Peter Handscomb (27) and Nick Larkin (22) appeared to have mounted a recovery with a stand of 36, only for the former to be run out chasing two as Mujeeb and De Villiers combined in the field.
Danger man Glenn Maxwell (1) followed three balls later as he was bowled by Swepson, who struck again to remove Nic Maddinson (9) and then Larkin after Nathan Coulter-Nile had fallen to Mujeeb for a duck.
That left the Stars on 92-7 and the tail never looked like mounting a remarkable recovery.
A TIGHT FINISH
In the fight for the final two playoff places, the Heat join the Scorchers on 12 points and would qualify as it stands, with Hobart Hurricanes and Sydney Thunder each a point back with a game to play.
Perth face the Thunder in their finale, while the Hurricanes visit Adelaide Strikers and the Heat face bottom side Melbourne Renegades.
The fight for the top five is going down to the wire.
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