In the battle between the two Midlands teams, Nottingham-based The Blaze were reeling as they slipped to 5-2 in the first over after being put in.
But Scotland international Sarah Bryce battled to 52 with useful contributions from Orla Prendergast (34) and Ella Claridge (38) in the middle order.
A valuable unbroken last wicket stand of 32 between Grace Ballinger and Charley Phillips got them up to 252-9 off their 50 overs.
With Abbey Freeborn and Davina Perrin at the crease, Warwickshire had reached 126-1 in reply.
But Kathryn Bryce removed Freeborn for 40 and Perrin for 53 in successive overs to change the momentum.
Nat Wraith and Charis Pavely came together at 157-5 and put on 46 to make the hosts favourites with less than 50 required, until Wraith sliced to point off Phillips for 34.
Then Kathryn Bryce did the rest, taking the last three wickets to quickly wrap things up with Warwickshire nine down and Chloe Brewer unable to bat as The Blaze moved to fourth, one place above their opponents.
