The leaders had resumed on 30 for two, but were reduced to 65 for eight with South African Abbott, who had removed both openers at the end of day one, taking his haul to nine for 40 from 18.4 overs as the visitors were skittled out for 142.
Batting proved equally tough for all but Hampshire captain James Vince (102 not out) as they reached a total of 176 for eight, leaving them 230 runs ahead.
— Hampshire Cricket (@hantscricket) September 17, 2019
Surrey had earlier lost their remaining six wickets for just 37 runs as they were bowled out for 174 with Jamie Porter and Sam Cook finishing with five each.
Kent will resume on two without loss in their second innings and with a lead of 215 over Yorkshire after a profitable day in the field at Headingley.
— Kent Cricket (@KentCricket) September 17, 2019
Having declared at 482 for eight, Kent set about the task of establishing a substantial first innings lead, and did just that with Matt Milnes' five for 87 helping to restrict the home side to 269.
Dominic Sibley century kept Warwickshire in touch as they attempted to chase down Nottinghamshire's first innings total of 498.
Sibley's unbeaten 115 provided the backbone with support from Sam Hain, who made 67 not out on the way to a closing total of 264 for two at Nottingham.
In Division Two, John Simpson blasted 167 not out as Middlesex scrapped their way out of trouble to leave champions Lancashire with a first innings deficit.
Having slumped to 39 for six overnight, Simpson, ably supported by James Harris, Toby Roland-Jones and Nathan Sowter, helped his side make 337, a lead of 78 which has been reduced to 64 for the lost of opener Alex Davies by stumps.
Half centuries from Richard Levi and Adam Rossington helped Northamptonshire establish a lead of 321 over Durham with four second innings wickets remaining.
Earlier, Ben Sanderson had picked up where he had left off, claiming six wickets for just 54 runs as the visitors folded for just 131 with only Ned Eckersley providing any resistance with a knock of 37.
Gloucester face a tense battle for victory over Worcestershire after wickets tumbled on day two.
The visitors will resume on 54 for four needing just 61 to win after securing a first innings lead of 14 before dismissing the home side for just 128 in their second innings.
Openers Luis Reece and Billy Godleman put on 274 for the first wicket as Derbyshire staged a second innings fightback at home to Sussex.
After seeing their side concede a 93-run first innings lead, Reece was run out for a career-best 184 while skipper Godleman remained unbeaten on 106 with the total standing at 360 for two at the close of play on day two.
Glamorgan wicket-keeper Chris Cooke fell four runs short of a hundred as bottom-of-the-table Leicestershire found themselves with a mountain to climb in Cardiff.
Cooke's 96 helped the home side to 435 all out in their first innings before Samit Patel and Ruaidhri Smith took three wickets each as the visitors were reduced to 191 for nine in response.