Spinner Mady Villiers gave Sunrisers the ideal start after the home side had chosen to bat at Beckenham, prising out Phoebe Franklin and Paige Scholfield in the space of three deliveries to leave them in trouble at 11-2.
But Smith and Davidson-Richards regrouped and got on top of the bowling as they amassed their marathon partnership, which finally ended when Jodi Grewcock tempted Davidson-Richards to hole out to long-off.
Smith also perished to the Sunrisers leg-spinner, who took 3-43, while Villiers (2-39) and Grace Scrivens (2-40) also helped to stifle the innings until Ryana MacDonald-Gray raised the scoring rate again late on.
MacDonald-Gray slammed Sophie Munro for successive sixes in her quickfire knock of 37 to ensure Stars topped the 250 mark – and they gained an early boost in defence of that total when the dangerous Scrivens pulled Franklin to deep square leg.
Jo Gardner (39) and Lissy MacLeod (44) built steadily with a second-wicket stand of 75, but Stars’ battery of spinners applied the brakes in the middle overs as the required rate began to rise above six.
Dani Gregory (3-47) made the breakthrough by bowling MacLeod with a top spinner and wickets began to fall rapidly, with both Gardner and Amu Surenkumar leg before attempting to sweep Smith.
The Stars captain finished with 2-31 and Eva Gray’s unbeaten 29 ensured that Sunrisers kept up the fight, but they were bowled out at the end of the 48th over.
At Lincoln, rain restricted the contest to 30 overs a side and Diamonds began brightly after being inserted, only to slump to 48-4 after losing four wickets for 10 runs, including two in successive balls to Cassidy McCarthy (2-42).
Bess Heath set about the rebuilding job with her third half-century of the tournament, sharing partnerships of 48 with Erin Burns and 58 with Beth Langston before Grace Ballinger had her caught at mid-off for 61.
Left-armer Ballinger (3-43) claimed two more quick wickets to stall Diamonds’ momentum, but the rain returned towards the end of their scheduled innings and the match had to be called off.