Kent 139 for 7 (Kuhn 29) beat Hampshire 88 (Stoinis 4-17, Milne 3-14) by 51 runs
Fast bowling duo Milne and Stoinis grabbed seven wickets between them to send Kent back to the top of the South Group of the Vitality Blast - after Somerset had temporarily overtaken them earlier on Friday.
Stoinis ended with figures of four for 17 while Milne celebrated three for 14 in the 51-run thrashing.
Heino Kuhn's 29, alongside Stoinis' 26 and Calum Haggett's quickfire 19, had lifted Kent to what still seemed a below-par score.
But needing 140 to win, Hampshire's chase began with a wobble losing their first three wickets for seven runs, inside 14 balls, and continued on a downward curve.
Milne was the chief early destroyer as he pocketed two scalps in two balls to see off James Vince and Sam Northeast.
Skipper Vince slashing a drive straight to Joe Denly at cover, before former Kent star Northeast was comprehensively bowled by the New Zealander.
Australian Stoinis then grabbed the attention of the over 7,000 strong Ageas Bowl crowd, by finding the outside edge of Colin Munro's bat - the opening batsman ending his stint at Hampshire with a disappointing six.
Rilee Rossouw and Tom Alsop were the next to fall, leaving Hampshire 20 for five, both collected by Stoinis. Liam Dawson and Joe Weatherley attempted to rebuild with a steady 22 stand for the sixth wicket.
But the collapse resumed when Weatherley spliced to cover, where Denly produced a Superman-like effort to swoop inches off the ground.
Kyle Abbott was dropped on a duck by Alex Blake, and by Sean Dickson on 10, but ran out of lives when he toed a flat-back shot to Kuhn at mid-off.
By the time Dawson was caught at deep square-leg, handing Stoinis his fourth wicket, the game had already petered out as a contest.
Denly bowled Chris Wood before pinning Mujeeb Ur Rahman as Hampshire were put out of their misery with 23 balls to spare, for their second lowest Twenty20 score of all-time.
Sam Billings had earlier won the toss and elected to bat first on a good, quicker than, track in lovely south coast heat and clear skies.
A running theme of the Kent innings would be a case of batsmen getting in with a few boundaries before getting out as they set an underwhelming, yet ultimately enough, 139 for 7.
Daniel Bell-Drummond started the trend by stroking Abbott through the covers before he was pinned by a low full-toss.
Fast bowler Abbott was making his first appearance in the competition since early July, where he had been taken for 95-runs in 7.2 overs, but looked rejuvenated when he found Denly skying to point for his second wicket.
Billings followed up his unbeaten 56 against Essex the previous night with a well-timed drive to get off the mark, only to falling into the curse and top edge a sweep to deep square leg.
The wicket was Dawson's first in a misery spin partnership with Ur Rahman - the pair's eight overs going at three for 43.
Dawson bagged his second when he bowled Kuhn, who top scored with 29, with a top-spinner, before Ur Rahman followed up with a wonderfully delivered googly as Blake was stumped.
Stoinis kept the innings ticking with 26 off 25 but he and Sean Dickson both mis-timed attempted pull shots into deep mid-wicket.
Kent had stuttered their way over 100, but Calum Haggett bumped up the score up to 139 with a 19 from nine ball cameo - which saw him smash the only maximum of the innings straight down the ground.