The hosts always had the threat of rain hovering over their chase, with heavy dark clouds constantly threatening the Utilita Bowl.
As such, keeping up with the DLS par score was crucial, while wickets would be decisive.
Hampshire losing both openers inside four overs made the job immediately more difficult as Southby (16) slapped to deep square leg, while Maia Bouchier (two) was caught at mid-off, a ball after being dropped at mid-on.
But Kemp arrived to turn the situation around.
The England all-rounder rampaged to 50 in 26 balls with a brutal display of hitting, with seven fours and a pair of sixes.
She moved Hampshire 10 runs ahead of the par score, but when she was bowled going back to Kalea Moore, the par rocketed from 77 to 103.
Adams, who had given Kemp free rein, now took control and pulled her side back to within touching distance of the rate with her standard range of ground strokes and gap finding.
Abi Norgrove’s tame chip to short midwicket for one once again put Hampshire 30 runs short, with play suspended for 20 minutes by rain.
Nancy Harman was leg-before for 13 on the other side of the delay, but Adams gained stickability from Naomi Dattani (22), with whom she put on 53, and then Taylor.
Taylor has continually proven herself a useful lower-order batter but belied her List-A best of 21, and with the unflappable Adams, the pair strode to the winning line with an unbroken century stand of 104, which fittingly ended with Adams cutting the winning runs for her 11th boundary.
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