Australian Klinger smashed an unbeaten 166, while Dent (142) scored his second hundred in this season’s competition in an opening stand of 242 to lead the hosts to 352-3 from their 50 overs.
Hampshire’s reply saw them finish up just short on a very creditable 342-8, thanks to half-centuries from Gareth Andrew (70no), Liam Dawson (57), Sean Ervine (53) and Tom Alsop (50).