Martin McCague took 5 for 3 in 17 deliveries, including his first hat- trick for the county, as the visitors lost their last eight wickets for seven runs in 44 balls, spanning 42 minutes.
Kent's second hat-trick in the match following Dean Headley's record- equalling third triple of the season on Saturday helped McCague to figures of 6 for 51 and he and Headley have now taken more than 100 Championship wickets between them this season.
Hampshire had looked in complete control at 143 for 1, with Kent's only success until then having come 50 minutes into the day when McCague trapped Jason Laney leg before for 14 with the total 25. Giles White and Paul Whitaker then added 118 for the second wicket before McCague started the rout bowling Whitaker for 53 with the total on 143.
Robin Smith went two runs later, also to McCague, and then the former England fast bowler got the wickets of Will Kendall, Adrian Aymes and Dimitri Mascarenhas to leave Hampshire struggling on 149 for 6.
Matthew Fleming polished off the tail with 3 for 0 in six balls as the Kent celebrations began in earnest.
A modest McCague said: "We have been doing the job for Kent all season and will keep doing so."
Graeme Hick's first century since he lost his England place helped Worcestershire to a five-wicket victory over Gloucestershire at New Road. Chasing 308 in 81 overs, they cruised home after Hick had made his 90th first-class 100 during a stand of 201 for the second wicket with Philip Weston, who scored 89.
Hick's old West Indian adversary Courtney Walsh caused the only problems as Worcestershire made the most of a career-best match return of 13 for 159 by their Australian captain, Tom Moody.Walsh yorked the opener Tim Curtis and returned after tea to dismiss the two top scorers in the space of 10 balls.Reuse content