Worcestershire were set a 399 victory target after Joe Denly scored a career best 227 for Kent on day three of the Specsavers County Championship clash at New Road.
Joe Leach's early two wicket burst and one for John Hastings reduced Kent to 205-6 – a lead of just 129.
But Denly and Adam Rouse added 149 in 39 overs – a Kent seventh wicket record in matches against Worcestershire.
They were eventually bowled out for 474 with Leach returning 4-79 to give him seven wickets in the game.
Then Worcestershire openers Daryl Mitchell and Brett D'Oliveira safely negotiated five overs in reaching 16-0.
Denly's score was also the highest by a Kent batsman versus Worcestershire, beating Leslie Ames' 201 not out at Gillingham in 1937 and 201 at New Road two years later.
Kent resumed on 120-3 – a lead of 44 – and Leach made a breakthrough in his second over of the morning.
Joe Weatherley had not added to his overnight 24 when he nicked the Worcestershire skipper through to Daryl Mitchell at second slip.
Joe Denly resumed on 67 and continued to impress although he had a let off on 81 when he edged Leach for four.
Leach struck again when Darren Stevens (19) offered no shot and was lbw with Kent then 169-5.
Hastings replaced Leach after an excellent morning spell of 7-2-21-2 and also caused problems.
Will Gidman was fortunate with a ball from the Australian which popped up on him and flew down to third man for four.
Denly went to his century with a six over long on off Moeen Ali from 145 balls with two sixes and 13 fours.
Hastings was rewarded for a good spell when Gidman went for a drive and was caught by Ross Whiteley at first slip.
Kent were 221-6 at lunch and Denly and Rouse dominated the afternoon proceedings via a century stand in 28 overs.
Denley reached 150 with a back foot push for two off Brett D'Oliveira.
The partnership exceeded the previous best for the Kent seventh wicket against Worcestershire of 110 by James Tredwell and Niall O'Brien at New Road in 2004.
The stand was finally broken to the last ball before tea with Rouse, whose 68 off 122 balls contained nine fours, caught by Whiteley at short leg off Moeen Ali.
Matt Coles hit a quickfire 39 before he top-edged a catch to keeper Ben Cox off Moeen.
Then Moeen pulled off a superb catch at deep backward square after Yasir Shah (27) had connected with a Hastings delivery.
The innings was wrapped up when Denly finally perished on 227 as he lofted Leach to Ed Barnard at long off. In all he batted for 468 minutes, faced 320 balls and struck 24 fours and five sixes.