Silk (46 from 25) took control at the fall of captain Moises Henriques' (57 from 37) wicket, with his side needing 44 from 23 to chase down the Heat's 7-164 at Metricon Stadium.
He fell with six balls remaining but by then his side only needed six runs off Ben Cutting's final over.
Tom Curran hit a full toss to the cover boundary from Cutting's second delivery and the visitors won with three balls and five wickets to spare.
The loss was the Heat's seventh straight and third in their current campaign and came despite a mature 84 from captain Chris Lynn.
Lynn was dropped on 13 and 73, while his first boundary sailed just wide of a diving mid-off as he built a relatively sedate innings.
The captain exploded once reaching the milestone, hitting five sixes to finish with 84 off 55 balls.
Lynn took it upon himself to build the inning after the early loss of local talent Max Bryant (34 off 17) stifled their momentum.
Bryant hit two huge sixes as he took to Sydney spinners Ben Manenti and Stephen O'Keefe in a nerveless first two overs.
Jimmy Peirson (23 off 17) joined Lynn with the Heat 5-91 in the 13th over and the paired steered the Heat to 163 before Lynn departed with three balls remaining.
Heat spinner Mujeeb Ur Rahman's second-over maiden put Brisbane in the box seat before Henriques and debutant Justin Avendano rallied.
A rookie error ended Avendano's (30 from 24) enterprising innings, run out by a Cutting direct hit when he failed to ground his bat while completing an easy single.
Henriques soldiered on though, before Silk's crafty knock improved them to 3-2 this season.