The Thunder recovered from 25-4 to post 134-4, with New Zealander Satterthwaite 57 not out and wicketkeeper Threlkeld unbeaten on 53 amidst a standout afternoon.
The 19-year-old later claimed a record four stumpings and affected a run out as Diamonds replied with 101 all out.
The Diamonds got off to a bright start in reply with a 43-run opening stand between captain Lauren Winfield and Australian Beth Mooney.
But they were two of four wickets to fall for 16 runs inside four-and-a-half overs as the score slipped to 59-4.
Both sides, who lost their opening fixtures on Sunday, had success with pace off the ball.
In the end, England left-arm spinners Sophie Ecclestone and Alex Hartley were the pick with 3-11 and 3-19 respectively, breaking a run of two successive Roses defeats.
After eight overs, this looked set to be a procession for the Diamonds as spin duo Chamari Atapattu and Katie Levick struck, while Alice Davidson-Richards’s medium pacers claimed two wickets in three balls in the seventh.
But left-handed Satterthwaite and Threlkeld then batted confidently, the pair reaching their fifties in the 19th over.
Winfield helped the Diamonds get off to a bright start in reply, twice handsomely driving Kate Cross for four, although she was dropped at point on 19 by Emma Lamb off the same bowler.
The England World Cup winner hit a brisk 28 before miscuing her international team-mate Ecclestone to mid-on at 43-1 in the sixth over.
That became 56-2 in the ninth when Mooney holed out to deep mid-wicket off Hartley.
Ecclestone then had Davidson-Richards stumped by Threlkeld at the end of the 10th before Hartley bowled Sri Lanka’s Atapattu at the start of the 11th.
The run out of talismanic England all-rounder Katherine Brunt in the 14th over following a mix-up with Delissa Kimmince left the score at 71-5.
Kimmince fell the same way before Threlkeld’s second stumped Thea Brookes. She then ran out Alice Monaghan and had Levick stumped off Danielle Hazell and Helen Fenby stumped off Ecclestone to wrap things up.