Chasing 174 for victory, the Heat needed 121 off the final 10 overs and looked beaten before Bryant (72 off 35) and Renshaw (48no off 33) added an extraordinary 108 off 51 balls for the fourth wicket.
Bryant and Renshaw enacted the power surge and took 21 off the first over bowled by Wes Agar and 12 from the next by Lockie Ferguson to give the hosts a shot.
The duo then went ballistic with an assortment of fours and sixes, with the hapless Agar coming in for particularly strong punishment, being plundered for a further 19 runs in his next over and ending with 1-61 from 3.5.
Bryant lashed four sixes and seven fours to be player of the match.
Matt Renshaw comples the winning run to ice the Heat's astounding comeback victory. (Darren England/AAP PHOTOS)
Monday night's boundary barrage ended a three-game losing streak for the Heat and took them to seven points, just two behind the top of the table Sydney Sixers.
"We needed 12 runs an over and we had to go for it there and then," Bryant told AAP.
"Me and Matty got a couple of balls away and momentum kept us going.
"Batting in the middle order suits my style and this was do or die for us."
Bryant said his side believed they could repeat last season's title win, but added that they "have to keep winning games".
Renshaw contributed a fine unbeaten 48 to guide the Heat home. (Darren England/AAP PHOTOS)
The Thunder, on eight points, will wonder how a game they had in the bag got away from them so quickly.
Veteran allrounder Dan Christian cam out of retirement to play a key role in lifting the visitors to a competitive total.
The 41-year-old put the coloured clothes on again to bolster the Thunder's stocks due to recent fielding injuries suffered by Cameron Bancroft and Daniel Sams.
His unbeaten 23 off 15 deliveries boosted the Thunder to 8-173 after they had slumped to 7-129.
Christian then dismissed the dangerous Nathan McSweeney on his way to 1-25 from four tight overs.
Recalled veteran Dan Christian contributed with bat and ball for the Thunder. (Darren England/AAP PHOTOS)
The Thunder's innings was held together by captain David Warner (50 off 35) who was in complete control until he was bowled trying to reverse sweep a yorker from Spencer Johnson (3-39).
Heat allrounder Michael Neser, 34, returned from a hamstring injury he suffered playing for Australia A in early November and struck in his second over to remove opener Oliver Davies (10).
It was Neser's 50th wicket for the Heat in his 100th BBL match.
Brisbane captain Colin Munro (23 off 25) became the 11th batter in T20 history to notch 11,000 runs but his BBL woes this summer continued.
The Thunder lost wickets at a steady rate as the hosts' pace attack of Neser, Johnson and Bartlett combined with success like they did in last season's run to to the title.
Johnson bowled with fire and regularly exceeded 140km/hr.
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