With the visitors requiring 10 to win off the final over, tailender Ben Hilfenhaus (10 off two balls) took matters into his own hands as he belted a four and a six off Ben Cutting (1-39 off 3.2 overs) to catapult the Hurricanes to the top of the table.
Hobart ended up on 7-210 which was the second Big Bash League record score set in the same night after the Heat amassed 3-209 only 90 minutes earlier.
Opener Ben Dunk top-scored for the Hurricanes with a blistering knock of 67 from just 33 deliveries which included five fours and four sixes, while Jonathan Wells (36 not out off 20), Travis Birt (27 off 20), Evan Gulbis (22 off 13) and Hilfenhaus all played important parts in the run chase too.
Champion New Zealander Daniel Vettori was the pick of the Brisbane bowlers with 2-32 off four overs and importantly bowled Dunk in the 12th over during a period of dominance for the Heat that saw them grab 3-13 at one stage.
Cameron Gannon (2-36 off four) was the Heat's other multiple wicket-taker but team-mates Dan Christian (1-29 off two), Alister McDermott (1-28 off two), Nathan Hauritz (0-25 off two) and Cutting came in for some serious punishment.
Earlier in the evening, the Heat looked on course for a huge win as Christian (70 not out off 40), Joe Burns (69 off 45) and wicketkeeper Craig Kieswetter (50 off 24) all plundered the Hobart bowling attack.
Christian smacked three boundaries and four sixes, Burns registered six fours and two maximums while Kieswetter was also fond of the direct route with six boundaries and three sixes to his name.
Doug Bollinger (1-27 off three), Xavier Doherty (1-33 off four) and Shoaib Malik (1-40 off four) were the only wicket-takers for the Hurricanes.
Doherty had Burns stumped by Tim Paine in the 18th over and ended the Heat number three's 97-run partnership with Christian which came off just 55 balls.
Malik also took the key wicket of Kieswetter whose strike rate exceeded 200.00.
Gulbis suffered the most damage of all the Hobart bowlers with his only over costing his side 22 runs.
Next up for Hobart is an engagement with the Melbourne Renegades at Blundstone Arena on New Year's Day while the Heat are also next in action against the Renegades at Etihad Stadium on Monday.