The Pakistan leg-spinner took 4-24, including the prized scalp of Matthew Renshaw, in a 34-run win after the hosts had posted 4-193 on Monday.
Brisbane were fresh off their jaw-dropping successful chase of 258 against Perth - easily the BBL's biggest - in which Renshaw and Jack Wildermuth scored hundreds.
Shadab had both batters clean-bowled attempting to sweep, picking up Wildermuth and fellow opener Colin Munro in his first over before Renshaw (43 off 28) was undone trying to reverse sweep.
Renshaw and emerging batter Hugh Weibgen (30 off 26) had steadied the innings in a 70-run partnership that had the Heat poised to chase down what would have been a Manuka Oval BBL record.
Weibgen then lapped a sweep into his own stumps and the chase, on a wicket keeping low and slow, was all but dead with five overs remaining.
Shadab made sure of it though, with another wrong'un beating an advancing Tom Alsop, who didn't even attempt to recover his ground.
Nathan McAndrew's maiden in the second over set the tone while Daniel Sams (2-25) was economical as the Heat finished on 6-158.
It was the Thunder's first win in their third game of the season, while the Heat fell to 1-2.
Earlier, Konstas (63 off 45) and fellow Thunder opener Matthew Gilkes (76 off 48) laid the framework in a 127-run stand.
Konstas hit boundaries to all corners of the ground while Gilkes punished anything on his pads.
Sam Billings (25 off 11) came and went with a bang and David Warner lasted just four balls for his seven.
But what looked likely to be another monstrous chase was wound back thanks to Wildermuth (2-25), Shaheen Afridi (1-35) and left-arm offspinner Matt Kuhnemann (1-29), who could find himself back in a baggy green on Boxing Day.
"Took a bit of time, but a good team performance. Hopefully we can go on from there," Konstas told Fox Sports of the Thunder's first win.
Gilkes has opened instead of Warner this season and was rewarded with a big score after promising starts in the first two games.
"He's an X-factor and has been smacking them the last few games, playing with absolute freedom and clarity," Konstas said.
"The wicket was staying a bit low, it was hard to hit the off-pace balls, so we were running really hard and trying to pick our moments."
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