Chasing Kent's 143 for eight, Hampshire were restricted to 135 for eight as they suffered their first defeat in 17 matches in the competition.
In a quirk of fate, their last loss also came at the hands of Kent in Southampton, when they went down by three runs in June 2012.
Despite the setback, Hampshire still lead the way at the top of the South group with Essex now their nearest challenges after they leap-frogged above Middlesex with a seven-wicket win over Sussex at Hove.
New Zealand opener Hamish Rutherford struck 84 from 43 balls to guide Essex to their target of 147 with 17 balls to spare.
Sussex had earlier made 146 for eight with Reece Topley taking four for 26, including three wickets in the final over.
In the Midlands/Wales/West group, Richard Levi crashed 70 from 43 balls as leaders Northamptonshire edged closer to a quarter-final spot after beating Worcestershire by five runs at New Road.
The big-hitting South African opener smashed six sixes and five fours before a lower order slump pegged Northants back to 137 for six, although that proved enough in the end.
Northants' position in the group was further improved as second-placed Glamorgan crashed to a comprehensive 10-wicket defeat to Gloucestershire.
Glamorgan were limited to 98 for nine batting first at Cheltenham and hosts Gloucestershire cruised to victory thanks to Chris Dent (63 not out) and Michael Klinger (35no).
Somerset claimed an even more convincing 10-wicket win over Warwickshire at Taunton to replace Glamorgan in second place and boost their hopes of appearing in a fifth straight Twenty20 finals day.
Yasir Arafat finished with four for five as Warwickshire were skittled for 73 - their lowest ever T20 total - and then Craig Kieswetter (39no) and Chris Jones (30no) saw Somerset race home with more than 11 overs to spare.
In the North group, Nottinghamshire moved top after beating Yorkshire by 25 runs at Headingley.
Chasing a target of 156, Yorkshire looked to be in with a good chance as Joe Sayers and Dan Hodgson put on 67 in 10 overs for the second wicket.
However, Notts' left-arm spinners Samit Patel and Graeme White soon broke through with some fine bowling to knock the stuffing out of the home side to leave last season's runners-up virtually without hope of qualifying for the quarter-finals.
Durham, meanwhile, beat Derbyshire by four wickets with eight balls to spare at Chesterfield thanks to Ben Stokes' 46 from 24 balls.
The Dynamos seemed to be heading for defeat at 36 for four in the eighth over chasing the Falcons' 136 for seven, but Stokes smashed five sixes and carried his side to the brink of victory with Gordon Muchall, who scored 37 from 27 balls, in a stand of 77 in eight overs.