Worcestershire wicket-keeper Ben Cox achieved his career best score as the home side set Kent a 266 victory target in the LV County Championship encounter at New Road.
Cox hit a superb 89 off 121 balls with one six and 14 fours before he was last out with the total on 270.
The 22-year-old surpassed his previous best tally of 65 made against Hampshire on the same ground last August.
Then Gareth Andrew and Jack Shantry made early inroads into the Kent second innings and reduced them to 51-3 from 22 overs by the close.
Cox came in at 113-5 and marshalled the lower order in ensuring the last five wickets added 157 runs.
Ross Whiteley and Shantry aided Cox in half century stands while last man Charlie Morris also dug in to ensure 32 crucial runs were added.
England national selector James Whitaker was present at the start of the third day when Worcestershire resumed on 41-0 from 17 overs – a lead of 36.
Doug Bollinger made a breakthrough for Kent when Daryl Mitchell (27) was caught behind by wicket-keeper Sam Billings to end a partnership of 53 with Matt Pardoe.
The next delivery accounted for Moeen Ali (0) who was adjudged lbw to a Bollinger delivery.
Tom Kohler-Cadmore confidently blocked the hat-trick ball and moved to 18 before being caught at mid-wicket by Brendan Nash off Tredwell for 18 with the total on 76.
Pardoe was solid in defence but also produced some impressive attacking strokes.
He advanced to 43, helping the lead to push past the 100 mark, but then was caught and bowled by Bollinger in his first over back in the attack at 110-4.
First innings top scorer Alexei Kervezee (21) was bowled by Mitchell Claydon in the last over before lunch.
Worcestershire resumed after the interval on 113-5 with Whiteley and Cox full of positive intentions.
Whiteley, who is in his first full season with the county after joining from Derbyshire, twice hit England spinner James Tredwell for six – over long on and then mid wicket respectively.
The half century partnership between Whiteley and Cox was achieved in just 13 overs.
Bollinger secured his fourth wicket by bowling Whiteley for 34 off 70 balls with two sixes and three fours wth the total on 168 and then Andrew was caught at mid wicket by Tredwell off Robbie Joseph for eight.
Four runs later Shaaiq Choudhry was also bowled by the Kent paceman to leave Worcestershire on 188-8.
But Cox took centre stage and two sweeps for four off Tredwell took him to his half century and he received staunch support from Shantry in a 50 partnership in 12 overs.
Bollinger took the new ball and the former Worcestershire player completed a five wicket haul on his Kent debut by trapping Shantry lbw.
Cox continued to mix attacking shots with farming the strike before he was last out for 89, bowled by Tredwell.
Andrew gave Worcestershire the perfect start when Kent launched their reply as Sam Northeast (0) fell lbw to the third ball of the innings.
The all-rounder accounted for Kent skipper Robert Key (13) in the same fashion and his opening spell realised excellent figures of 7-4-15-2.
It became 32-3 when Daniel Bell-Drummond (14) became the third lbw victim of the innings, to Shantry.