Gloucestershire 352 for 3 (Klinger 166*, Dent 142) beat Hampshire 342 for 8 (Andrew 70*, Dawson 57, Ervine 53, Alsop 50) by 10 runs
The holders had lost their first three group matches. But an opening stand of 242 in 38 overs between Klinger and Dent led the hosts to 352 for 3 from their 50 overs and ensured points on the board at last after the visitors had won the toss.
Dent outscored his captain to make his second ton in this season's competition off 116 balls, with 14 fours and three sixes, while Klinger went on to a career-best List A score off 150 balls, with 16 fours and six sixes.
In reply, Hampshire managed a creditable 342 for 8 without ever looking like winning. Gareth Andrew contributed 70 not out, Liam Dawson 57, Sean Ervine 53 and Tom Alsop 50.
Dent was in top form from the outset with a series of sweetly-struck boundaries through the off-side. The left-hander has rarely looked better as he moved to a brilliant 95-ball hundred, with Klinger content to play a supporting role.
The Gloucestershire skipper only took charge after Dent had fallen to a skied catch at extra cover by Shahid Afridi off Dawson at the end of a memorable innings.
From then on Klinger moved into top gear himself, reaching his 15th List A century off 115 deliveries. He then smacked a six and two fours in an over from Ryan Stevenson as the 300 was brought up in the 45th over.
Klinger passed his previous best List A score of 140 not out by blasting his biggest six off Tino Best, the ball smacking against the top floor of the flats at the Ashley Down Road End.
Ian Cockbain contributed a breezy 29, but it had basically been an exhilarating two-man show as Gloucestershire took a grip. Only Afridi, who conceded 44 from ten overs, exerted any measure of control.
Hampshire began their reply solidly with an opening stand of 41 before Jimmy Adams fell to Liam Norwell for 22.
Alsop went on to an impressive half-century off 39 balls, with five fours and a six, but the very next delivery from Benny Howell saw him carelessly drive a catch to extra cover.
Ervine blasted successive sixes off Howell in the 19th over as he moved to the quickest fifty of the match off 32 balls, with three sixes and two fours.
Will Smith helped add 78 in 11 overs before driving Kieran Noema-Barnett to mid-on where Tom Smith initially fumbled, but grabbed the ball at the third attempt.
Noema-Barnett then struck the key blow with his innocuous looking medium-pace as Ervine miscued a cross-batted shot to short fine-leg. And Hampshire's last realistic hope was dispelled when Afridi fell cheaply to Craig Miles.
Dawson's 47-ball half-century and Andrew's blistering late assault were spirited efforts, but too little too late as 30 were still required off the final over. Andrew picked up two more sixes in it to take his five in a 41-ball blitz that deserved more reward.