After being sent in at Allan Border Field on Wednesday, the Heat's impressive total of 5-184 was set up by opener Redmayne (70 off 53) and No.3 Heath (51 off 26) in a 92-run stand for the second wicket.
The Hurricanes started well in pursuit and were 0-48 in the sixth over before the Heat bowlers turned the screws with relentless pressure to bowl the visitors out for 131.
Heat skipper Jess Jonassen (4-20) returned her best figures for the season.
The Heat went to 14 points on the ladder, equal with Perth at the top with Sydney Thunder (13 points) and Adelaide Strikers (12 points) playing later on Wednesday.
England wicketkeeper/batter Heath was given her first opportunity up the order and made the most of it with a blazing knock.
The visitors had a shocker in the field to start the innings and dropped five catches.
Heath was a beneficiary. Given an early life, the 22-year-old was in an aggressive mood.
Her strength square of the wicket came to the fore with strong pulls and cuts. She was also severe on the spinners and lofted Ruth Johnston for consecutive sixes down the ground.
"There had been discussions around putting me in early during the powerplay to try and play that hitting role," Heath told AAP.
"I like to create momentum and go after the ball.
"They backed me to go out and play my style of cricket so it was good to get some runs and a win."
Player of the match Redmayne played the type of innings she made her own last season for the Heat when she was the side's leading run scorer. She drove elegantly, cut and pulled clinically and ticked over the strike.
Former South Africa captain Mignon du Preez (26no off 15) played a handy late cameo for the Heat against her former team.
Hurricanes opening bowler Shabnim Ismail (2-22 off four) was impressive for the visitors.
Lizelle Lee (24 off 18) and Bryony Smith (28 off 19) gave the Hurricanes a blistering early start in the run chase but once they were dismissed wickets fell regularly.
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