England's Nat Sciver-Brunt hit a match-winning 66 not out at Edgbaston as The Blaze won for the seventh time in 11 games to go further clear in the Rachael Heyhoe Flint Trophy standings.
The all-rounder rescued her side from 91-6 to edge the top-of-the-table match with Central Sparks by three wickets.
In another tight finish, Northern Diamonds' Hollie Armitage hit a century but just failed to get her side home.
Southern Vipers triumphed by three runs while Thunder and Sunrisers also won.
"As long as Nat was there, we knew we were in an all right position," said Blaze captain Kirstie Gordon.
"That's a lot of weight on one person's shoulders but, when you are as good as she is, she keeps delivering.
"Good teams win from tricky positions like we did. Last year and the year before we would never have won that game, we would have crumbled, but we stuck in there and came through.
"We are in a really good position now to go through. The team is going to look a little bit different next week with England and Scotland commitments, so it was really important to win when we had a full-strength team out."
The Blaze go 11 points clear at the top on 38, with three games left.
Sparks stay second on 27, but are now only a point clear of third-placed South East Stars (26), with Southern Vipers (23), Thunder (22), Northern Diamonds (21) and Sunrisers (20) all still in contention.
Nat keeps her nerve
Bethan Ellis (53) and Katie George (50) both made half-centuries as The Blaze bowled out Central Sparks on their own patch for 189, Josie Groves taking 3-39.
The Blaze reply was then spectacularly launched by Lizelle Lee (40} before Sciver-Brunt, making her first RHF Trophy appearance since 2021, showed all her experience and class in a 71-ball knock to see Blaze home to 193-7 off 45.1 overs.
She shared a key stand of 40 in 11 overs with Higham (20), who fell to a stunning catch by Green at mid-wicket.
Sciver-Brunt then found another reliable partner in Gordon, who made an unbeaten 15 in an unbroken stand of 62 in 90 balls.
Diamonds come so close to victory
In the day's other tight finish, centurion Hollie Armitage was left stranded on 106 as Northern Diamonds just failed to beat Southern Vipers in a game of over 500 runs.
Skipper Georgia Adams made 82 as the Vipers set a challenging total of 261-8 from their 50 overs.
But, although the Diamonds looked like chasing it down, the Vipers hung on, taking key wickets at crucial times, including one for Adams.
It left eight runs needed from the final over and Georgia Elwiss kept her head with six excellent deliveries.
After Armitage took one off the first, she bowled Leah Dobson off the second and then only conceded four more singles.
Thunder find their touch at Guildford
Thunder earned only their second victory of the competition as they beat South East Stars by six wickets at Guildford to keep alive their hopes of a play-off place.
Spinners Olivia Bell (4-23) and Fi Morris (3-33) were the stars at Woodbridge Road as they bowled out the hosts for 145, of which Paige Scholfield top scored with 38.
England opener Emma Lamb then led the way with 50 as Thunder reached their target on 147-4.
Naomi Dattani chipped in with 25 in a 65-run stand with Lamb, who fell lbw to Alice Davidson-Richards without further addition.
After Dattani was caught off spinner Dani Gregory in the next over, a 43-run stand between Fi Morris (18) and skipper Ellie Threlkeld (22*) helped Thunder over the line in the 26th over.
Sunrisers win battle of the bottom two
Sunrisers climbed off the foot of the table as they beat Western Storm by four wickets in the battle of the bottom two at Radlett.
It avenged their six-run defeat by Storm at Cheltenham in July as Sunrisers' ruthless bowling paved the way to their third win in 11 games.
Storm never really recovered from being reduced to 18-4 by Kate Coppack's early three-wicket burst.
Emma Corney made 34, but the Sunrisers spinners (Jodi Grewcock 3-24, Mady Villiers 2-31) and Grace Scrivens (1-19} restricted them to just 143 all out in 45.1 overs.
Villiers then top scored with 29 off 24 balls, while Grewcock, Amara Carr and Jo Gardner all made 24 as Sunrisers reached their target on 144-6 with 16.1 overs to spare.