Kieswetter, who this week signed a new three-year contract with the county, passed 50 for the sixth time in 10 matches in this season's competition and his 60 guided Somerset to a score of 155 for four batting first at the Ageas Bowl.
That was less than the visitors looked like getting at one stage, but proved more than enough as tight bowling and good fielding helped dismiss Hampshire for 116 with 22 balls to spare.
It was only Somerset's fourth win of the season yet it still enabled them to complete the double over 20-over specialists Hampshire and move up to fifth in the standings.
Somerset chose to bat first on a blameless wicket but lost captain Marcus Trescothick in the second over, nicking Chris Wood to wicketkeeper Michael Bates for two.
Hampshire could hardly have wished for a better start, although Kieswetter then shared stands of 55 for the second wicket with Peter Trego and the third with Alviro Petersen, who was 38 not out at the conclusion of the Somerset innings.
Kieswetter's 60 - which left him second only to Surrey's Jason Roy in the Blast run-scoring charts - came off 44 balls and included five fours and two sixes before he perished to Matt Coles while attempting another extravagant drive.
That meant Somerset were 115 for three; however, Petersen and James Hildreth saw their side somewhat sedately through to the last ball of the innings - at which point the latter was caught on the midwicket boundary to leave Hampshire needing 156 for victory.
The hosts suffered a nightmare start as captain James Vince went to the first ball he faced, playing around a Trego delivery to be trapped lbw.
The wickets then continued to tumble as Hampshire's top-order collapsed in an uncharacteristic panic, and midway through the eighth over they were 41 for six.
Jimmy Adams fell to a catch at mid-on, Will Smith lifted Alfonso Thomas to Petersen at midwicket and then came a double run-out catastrophe in the sixth over to swing the match irreversibly Somerset's way.
First Glenn Maxwell was left stranded going for a second and then Michael Carberry, who might have been responsible for Maxwell's exit, went the same way, beaten by a throw from Thomas at short fine-leg chasing a cheeky single.
When Sean Ervine strayed from his crease off leg-spinner Max Waller's third delivery and was stumped by Kieswetter, Hampshire were as good as finished, and so it proved despite a lower-order fight.
Coles and Wood battled bravely in an innings-best stand of 42 for the seventh wicket before the former holed out to Waller, also at midwicket, and Hampshire were 88 for eight when Wood lifted Thomas to Dirk Nannes in the deep.
Abbott and Bates took Hampshire past the 100 mark but the end was not long in coming, to the dismay of a large home crowd, as Nannes wrapped things up with the wicket of Bates.