Replying to Hampshire's first-innings 274 all out, captain Klinger struck eight fours and a six in his unbeaten 53, while Dent provided valuable support in his 37 not out.
Thilan Samaraweera completed his first century for Worcestershire against Leicestershire at New Road.
The Sri Lanka batsman struck exactly 100 before Daryl Mitchell promptly declared the home side's innings on 320 for seven.
Leicestershire had reached 55 for one in reply by lunch.
There was no play possible before lunch at Old Trafford, with the match into its final day.
A draw seems to be the likely outcome in the clash between Lancashire and Essex, who may opt to declare on 203 for three and set the Red Rose a victory target of 253.