The Diamonds’ slim hopes of qualifying for Kia Super League Finals Day at Hove later this month remain alive after chasing down a target of 67 to jump off bottom spot with a second win from eight games.
Australian opener Beth Mooney led the chase with 44 not out off 30 balls, including eight boundaries, as the five-point win was completed with 10.3 overs remaining.
But they must win their last two fixtures against Lancashire at Blackpool on Tuesday and Loughborough at Emerald Headingley on Saturday to have any chance of a top-three finish.
Surrey, invited to bat, slipped from 33-1 towards the end of the seventh over to 41-5 early in the 10th and were bowled out for 66 in 16.4.
Seamer Beth Langtson starred with 3-14 from 3.4 overs and Australian overseas all-rounder Delissa Kimmince 2-14 from three with her seamers.
Leg-spinner Katie Levick struck twice in two overs, while miserly Katherine Brunt claimed a wicket and picked up a direct hit run out.
It was the second lowest total in KSL history, with Yorkshire posting 64 in defeat to Southern Vipers in 2016.
Surrey rested Sarah Taylor and missed her as they crumbled amid some scrambled shot selection against a sharp Diamonds outfit with the ball and in the field.
Gwen Davies took a particularly smart catch running back from backward point and diving to help Kimmince remove Marizanne Kapp in the fifth over to leave Surrey 26-1.
Brunt later swooped at mid-wicket and threw down the stumps at the non-striker’s end to leave Hannah Jones short as the score fell to 66-9.
The crucial period started when Kapp fell, and she was followed by Lizelle Lee, who was caught at deep cover off Alice Davidson-Richards.
Kimmince then had Stars captain Nat Sciver lbw on the sweep before Langston had Sophia Dunkley caught behind.
Langston later bowled Mady Villers and had Eva Gray caught behind to wrap up the innings.
South Africans Lee and Kapp, with 13 apiece, were the only two Stars batsmen to reach double figures.
Sciver then conceded five wides down the leg-side with her first ball at the start of the second over as the hosts got their chase off to a flying start at 22-0 after two and 49-0 after six overs of power play.
Mooney, who earlier took two catches behind the stumps, prospered as Sciver in particular erred in line and length.
Off-spinner Laura Marsh picked up the only wicket when Lauren Winfield (14) chipped her to long-on (55 for one in the seventh).
Both Yorkshire’s wins this campaign have come at this fast-scoring Clifton Park venue. They are now within six points off Surrey in third.