Nat Sciver-Brunt hit 31 from 25 balls in her first domestic appearance in England in nearly two years
The Blaze overcame Lancashire to remain unbeaten and close the gap at the top on Women's T20 Blast leaders Surrey as Hampshire also won to remain in touch.
Australia's Heather Graham collected 3-36 as The Blaze restricted Thunder to 150-9 at Leicester.
Scotland's Ailsa Lister provided the main Lancashire resistance with a superb 79 from 38 balls.
The hosts were in a spot of bother at 84-4 in the 12th over when England skipper Nat Sciver-Brunt departed for 31 in her first domestic appearance since 2023.
But Georgia Elwiss hit an unbeaten 43 to steer them over the line with 10 balls to spare and five wickets in hand.
At Taunton, Freya Kemp smashed an unbeaten 65 as Hampshire posted 169-6 and, despite 60 from Niamh Holland and 43 from Amanda-Jade Wellington, the winless hosts' brave chase fell five runs short.
After being asked to bat first, Thunder struggled to 29-2 in the six-over powerplay but Lister had an escape when she was dropped at mid-wicket on three.
Thunder were 65-4 in the 12th over but the fifth-wicket pair of Lister and Fi Morris (22) almost doubled the total before the latter hit Graham straight to backward point with 15 balls to go.
Alana King, Kate Cross and Tara Norris went without scoring and Lister, dropped again on 62, eventually fell to the final ball from Graham, having hit the Australian for six twice in addition to nine fours in her 79 – the highest by the team this season.
The Blaze lost Tammy Beaumont and Kathryn Bryce early in the reply but Sciver-Brunt hit four of her first 10 balls to the boundary and the hosts looked comfortable at the halfway point, needing 78 to win.
Sciver-Brunt missed a straight ball from Grace Potts to depart and England colleague Amy Jones followed for 16 soon after but three fours from Graham (19*) regained momentum and Elwiss hit her seventh four down the ground to win it.
On a scorching day at Taunton, Hampshire openers Maia Bouchier and Charli Knott put on 80 before Chloe Skelton took a fine catch over her shoulder at mid-on to send Bouchier on her way for 43 from 26 balls with eight boundaries.
In her final game before returning to Australia, Knott holed out to international team-mate Wellington at long-on 10 balls later for 43 from 34 balls.
Georgia Adams (10) and Rhianna Southby fell in successive deliveries to Charlie Dean (3-25), while Abi Norgrove was run out in the next over.
But Kemp went through the gears, with seven fours and two sixes in her 38-ball stay which guided the visitors to 169-6.
Seeking their first win in their seventh match, Somerset fell to 19-2 after four overs but Holland shared a stand of 52 with Sophie Luff (23) and then 63 with Wellington on her way to a career-best T20 innings of 60 from 53 balls, to set up a tense finale.
Wellington hit 44 from 25 balls but fell in the final over as the hosts came up just short at 164-6.
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Women's T20 Blast: Blaze and Hampshire Hawks boost Finals Day hopes – BBC
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