COUNTY CHAMPIONSHIP DIVISION ONE, Canterbury:
Hampshire 204 & 355-9 dec beat Kent 182 & 247 by 130 runs
Hampshire 20pts, Kent 3pts
Cork has taken 45 Championship wickets for Hampshire this season
Hampshire bowled Kent out with just five minutes to spare at Canterbury to earn a 130-run win and confirm their Division One survival.
Dominic Cork took 4-43 and Danny Briggs 4-93 as Kent were dismissed for 247, despite the efforts of Sam Northeast (71) and Darren Stevens (45).
Earlier, Hampshire declared on 355-9 to set the hosts a notional 378 to win.
Kent must now win at Headingley against Yorkshire next week and hope Hampshire beat Warwickshire to survive.
Kent are only able to overhaul the Bears because, even though they can finish level on points and number of wins with Hampshire, the men from The Rose Bowl have a batter head-to-head record.
Hampshire batted for a further hour on the final morning, with James Vince moving to 68 not out, to leave Kent a minimum of 81 overs to reach their improbable target.
The chase was over almost as soon as it began, with Joe Denly and Rob Key falling before lunch to Cork and Briggs respectively.
Kent's position worsened after the break when Martin van Jaarsveld and Geraint Jones fell in quick succession, but Northeast combined with Darren Stevens (45) for a fifth-wicket stand of 81 that gave the hosts hope of claiming a draw.
But, after tea Stevens was bowled by Cork and Northeast was trapped lbw by James Tomlinson to send Kent on the way to defeat.
Blake, dropped on 12 and 30, chipped Briggs to Vince to become the first of the the final four Kent wickets to fall for 18 runs.
As Hampshire rushed round to bowl more overs before the 1730 BST close, James Tredwell gloved Briggs to wicketkeeper Michael Bates, Cork had Matt Coles caught off a leading edge and, with only one over remaining, Simon Cook fended Tomlinson to short leg.