The Heat posted 8 for 163 and dismissed the Renegades for 137 at Adelaide's Karen Rolton Oval.
It was the Brisbane outfit's second win in three days over the same opposition after prevailing in Mackay on Tuesday.
The Heat slumped to 3 for 31 at the end of the sixth over before Voll (52 off 37 balls) and Amelia Kerr (27 off 22) conjured a rescue mission to get their side back in the game.
Voll's innings was a masterclass of placement and common sense in a knock that included nine boundaries.
She stayed until the 19th over to hold the innings together with late cameos from Jess Jonassen (16) and Pooja Vastrakar (13no) giving the Brisbane bowlers a total to defend.
The Renegades' innings was a carbon copy of the Heat's at the start as they crashed to 3 for 15 in the fifth over.
Melbourne needed 99 from the last nine overs and a whirlwind hand by Ellie Falconer (27 off 11) gave her side a chance before she chopped on to Kerr. Courtney Webb (47no) ran out of partners when the last wicket fell at the end of the 19th over.
The Heat's bowlers performed well as a unit with legspinner Kerr (3-26) and offspinner Charli Knott (3-19) chiming in with key wickets to swing the momentum their team's way.
The Renegades announced on Friday that they had signed Sri Lanka captain Chamari Athapaththu for the remainder of the season.
The 32-year-old will join the squad following Monday's match against the Adelaide Strikers, and she replaces Indian skipper Harmanpreet Kaur, who was ruled out for the season with a back injury.
Meanwhile, the dates for the WBBL finals have been confirmed, with all three matches to take place between November 23-26.
The Eliminator (3rd v 4th) is on November 23, with The Challenger (2nd v The Eliminator winner) to be held a day later.
The November 26 final is on the same day as the Socceroos' World Cup clash with Tunisia, and also the Victoria State election.