Rain saw the match reduced to 13 overs per side, before Atapattu's 66 off 40 balls helped the Diamonds post 110-5.
England seamer Katherine Brunt took two wickets in two overs, bowling Amy Jones and trapping Ellyse Perry lbw, as Lightning fell to 13-2.
Georgia Elwiss hit 41 but could not stop her side falling to a 17-run loss.
Sri Lanka all-rounder Atapattu's 66 not out, which included nine fours and two huge sixes, was her first half-century since she smashed an unbeaten 178 in the World Cup against Australia in June.
The 27-year-old also took 2-11 in three overs, bowling Australian opener Elyse Villani before having Lightning captain Elwiss caught at cover, as the hosts struggled at Haslegrave.
A third loss of the tournament for Lightning, who reached last year's Finals Day, leaves qualifying for the knockout stages unlikely.
An unbeaten half-century from Chamari Atapattu led Yorkshire Diamonds to victory over Loughborough Lightning in the women's Super League.