Hampshire moved back to the top of the Division Two table with a 278-run victory after Leicestershire's collapsed on the final day.
Set a target of 375 at Grace Road, Leicestershire were bowled out for 96 shortly after lunch.
Opening batsman Greg Smith top scored with 39 but four of the top seven made ducks in an innings lasting 31.4 overs as Hampshire spinner Danny Briggs finished with 4-13 and seamer Matt Coles 3-24.
Coles had earlier hit 83 off 77 balls at No 8 before being stumped off Jigar Naik's bowling, prompting Hampshire to declare their second innings at 338-9.
Hampshire's 22-point haul means they go back above Worcestershire - who beat Essex the previous day - for first place in the lower tier.
At Bristol, Gloucestershire completed a 290-run victory over Kent on the final day, their first win of the season.
Kent resumed on the fourth morning at 165-5 in pursuit of a target of 582 and, despite Ben Harmison's career-best 125, they lasted only 36.4 overs before being all out for 291.
Harmison, on 66 overnight, extended his sixth-wicket stand with Sam Billings to 139 before Billings was bowled by Matt Taylor for 67.
Taylor (3-55) followed up by removing Adam Ball with his next delivery and - although Harmison brought up his sixth first-class hundred from 175 balls - the end came quickly thereafter.
Harmison was ninth out, caught in the covers by Michael Klinger off James Fuller's bowling, while Will Gidman finished with 3-54 to take his match tally to seven wickets.
The result moves Gloucestershire up to sixth in the Division Two table, four points behind fifth-placed Kent.