Freya Davies (2-15) and Bex Tyson (2-20) starred with the ball for Hampshire as Essex fell short of a target of 102, finishing on 97-6.
Earlier, Maia Bouchier and Freya Kemp both made 31 in what looked an under par score of 101-7, Esmae MacGregor the pick of the home attack with 2-17.
In reply, Sophie Munro top-scored with an unbeaten 28 but Hampshire eked out a narrow win to all but mathematically assure their semi-final spot.
At Emirates Old Trafford, an impressive bowling display set Somerset up for victory against second-placed Lancashire.
They restricted their hosts to 169-9 from 44 overs and, after a 90-minute rain delay, chased a revised 164 from the same allocation inside 35 for a bonus point.
Ellie Anderson’s seam accounted for three wickets and Amanda-Jade Wellington’s leg-spin two before Niamh Holland and unbeaten Gibson contributed 44 apiece.
Wellington also added a steadying 25 not out to cap her impressive day.
Inserted Lancashire had been put under early pressure at 69-7 inside 24 overs before England seamer Kate Cross’ composed 51 off 58 balls led a fightback which ultimately failed to prevent defeat.
It was a frustrating day in Birmingham for Warwickshire and Durham, who both needed maximum points to boost their slim Finals Day chances, only for rain to prevent any play at all.
At Trent Bridge, meanwhile, The Blaze, in third, and fourth-placed Surrey had to settle for two points each in their quest for semi-final places.
Surrey had the hosts in trouble as Alexa Stonehouse took 2-23 but the weather intervened to preclude further play.
