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Southern Vipers 142 for 5 (Wyatt 76, Higham 3-30) beat Lightning 141 (Kelly 36, Higham 31, Elwiss 3-28)
England opener Danni Wyatt cracked 76 from 44 balls at Trent Bridge as Southern Vipers made it four wins from four in the Charlotte Edwards Cup, which all but guarantees their place at next month's finals day.
Lightning, who suffered a third defeat in four, were bowled out for 141 in 19.4 overs, Vipers chasing down their target in the 17th to win by five wickets.
Wyatt hit 11 fours and a six before she was caught by England team-mate Tammy Beaumont on the midwicket boundary with Vipers in sight of the win.
Wyatt, whose maximum was driven over mid-on, was dropped twice, on 61 and 65, although both were difficult chances in the deep and it is debatable whether it would have altered the outcome had one of them stuck.
After Lightning had won the toss, Kelly shrugged off the loss of opening partner Beaumont, clearing the leg-side boundary three times off Lauren Bell before cracking three consecutive fours off Kemp.
She and Ella Claridge added 44 in 19 balls but Lightning's blistering start was checked by the loss of three wickets in seven balls on the same score.
England hopeful Bell went for 28 in two overs but the introduction of Anya Shrubsole saw Claridge brilliantly caught by Bell at short third before new batter Sarah Bryce clipped tamely to short midwicket.
Kemp had dismissed Beaumont caught behind as she sought to drive the teenager's first ball, and claimed another big scalp as Kelly was pouched by a back-peddling Maya Bouchier at midwicket at the start of her third over. With that, Lightning had slipped from 52 for 1 to 52 for 4 in the blink of an eye.
Bryce, the experienced Lightning captain, took charge of the rebuilding job but her side were 77 for 6 in the 10th over after Elwiss had Bethan Ellis caught at backward point before Teresa Graves was leg-before trying to sweep Vipers skipper Georgia Adams's offspin.
Bryce fell for 23, hitting Elwiss to extra cover, but Higham and Sophie Munro added a valuable 33 for the eighth wicket before Paige Scholfield held on to a catch falling backwards at long-on to give Elwiss her third scalp as Munro departed.
Higham ultimately hit Bell straight to mid-on and Grace Ballinger sliced to short third as the Lightning innings ended after four balls of the final over.
Needing just over seven an over, Vipers were 48 for 1 from the powerplay after Adams was caught at point but Wyatt showed her quality as she and Bouchier added 69 for the second wicket before 17-year-old leg spinner Josie Groves had Bouchier caught at mid-off.
Wyatt holed out to midwicket and Scholfield top-edged to cover as Higham took two in three balls to induce a minor wobble from the Vipers, who lost Elle McCaughan as Higham picked up her third scalp via a stumping but the result was never in doubt.