The 21-year-old snared 3-22 in four overs to turn the game after the Renegades started fast in pursuit of the Heat's 8-169 at Allan Border Field.
The win marked the first time in WBBL history that the Heat had started a season with consecutive wins.
The Renegades made a blistering start courtesy of West Indies gun Hayley Matthews (35 off 28) before Parsons captured two wickets in her opening over, the 21-year-old's first victims in the WBBL.
It got better for Parsons when allrounder Deandra Dottin (1) was controversially given out lbw after the ball had deflected off her glove and onto the pad.
Dottin called for a review but there was no DRS in this match, although 33 out of 43 WBBL games this season will feature the review system.
The Renegades fell apart with opener Courtney Webb (25) run out and skipper Sophie Molineux (0) both out in the 10th over as the visitors slumped to 5-71 after being 0-51.
The Heat turned the screws with seamer Shikha Pandey (2-27) continuing her excellent start to the season to restrict Renegades to 9-141 despite a quickfire 38 from Naomi Stalenberg.
Parsons suffered a shoulder injury last year and missed the entire WBBL season after she was Queensland's leading wicket taker in the WNCL.
Such is her talent she recently won Australia A selection against India ahead of what looks set to be a fruitful career.
She said learning off former Heat legspinner and New Zealand's T20 World Cup star Amelia Kerr had helped with her craft.
"Learning off Amelia the last three years has been really special because she is the best to do it," Parsons told AAP.
"Our spin bowling coach at the Heat is Cameron Boyce and he is amazing at what he does and it has been really cool to pick his brain.
"It was a long countdown to Big Bash but I got here in the end and it was super special to play my debut game at Allan Border Field."
Earlier, experienced Heat duo Georgia Redmayne (44) and Lauren Winfield-Hill (24) added 66 from 46 to set the innings up.
Redmayne was savage square of the wicket and pulled her first four boundaries stylishly.
Winfield-Hill rotated the strike while punishing anything loose. One stylish reverse sweep rocketed to the fence of spinner Georgia Wareham before the Englishwoman was well caught at mid-wicket.
Charli Knott, player of the match against Adelaide Strikers in the season opener, holed out for just one before Dottin drew an edge from Redmayne and the hosts slipped to 4-86.
Swashbuckling Laura Harris (31 off 16) upped the ante as only she can with a quickfire innings during the power surge that included a cut over point for six.
Heat skipper Jess Jonassen finished unbeaten on 25 to get the Heat to a competitive total.
The West Indian connection of Dottin (1-27) and Matthews (2-21) dried up the runs and took key wickets for the Renegades.
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