Clarke scored five Championship hundreds last summer and had firmly established himself as a member of the England Lions side for the past 18 months.
But the 21-year-old has struggled to build on several promising starts this summer until today as he oozed class and composure in making 142 off 197 balls with 22 fours.
His efforts were largely responsible for Worcestershire obtaining a first innings lead of 76 as they were bowled out for 336 in the Division Two promotion battle despite a six wicket haul from Matt Coles.
Then 19-year-old Tongue, who is in his first season of senior cricket, again demonstrated his potential by picking up two wickets in his initial five over burst.
He is still a work in progress but now has 26 Championship wickets to his name and troubles batsmen with his pace and ability to extract bounce.
It left Kent ending the day on 120-3 a lead of 44.
But Worcestershire will not want to chase a substantial target in their final innings as Pakistan spinner Yasir Shah is likely to pose an increasing threat during the latter half of the game between the second and third places teams.
Clarke was significantly aided in Worcestershire recovering from 48-3 by George Rhodes – making his first appearance of the campaign – and skipper Joe Leach.
Rhodes, occupying the number five slot previously held by the departed Tom Kohler-Cadmore, figured in a stand of 131 in 33 overs before on 45 he edged Coles to Will Gidman at second slip.
It was the only wicket to fall in the morning session but Shah quickly got to work as Ben Cox (19) and Ross Whiteley (0), the latter attempting an ugly swipe across the line, were trapped lbw.
Barnard (16) was unfortunate to be run out as Gidman deflected Clarke’s drive onto the stumps at the bowler’s end and at 240-7, Worcestershire were still 20 runs in arrears.
But not for the first time in adversity, Leach proved a willing ally as he dominated an eighth wicket stand of 90 in 17 overs.
Four boundaries in one over from Gidman steered Worcestershire into the lead and he reached his half century off 55 balls with a straightsix off Denly.
The stand was broken the final ball before tea when Clarke was caught behind off Coles who then mopped up the innings by accounting for John Hastings and Tongue to finish with 6-84 from 18.4 overs.
Leach finished unbeaten on 57 and was soon at work with the ball in his first over as Daniel Bell-Drummond (0) edged through to Cox in his first over.
Tongue came into attack and Sean Dickson (12) provided Cox with another catch and then captain Sam Northeast (14) was yorked.
Joe Denly ensured there were no more alarms for the visitors with an unbeaten 67 but there is work to do before Shah will have a realistic total to work with.
Kent head coach Matt Walker said: “It is a better position than we were in about an hour before stumps. I fought we pretty hard during the course of the day.
“As was the case in our innings there were patches when they scored quite freely and then us clawing it back and bowling in good patches and then wickets coming in a bit of a cluster.
“We didn’t want to lose three wickets this evening. We hoped one, maybe a maximum of two, but the two Joes (Denly and Weatherley) played really well at the end and stuck in really well.
“To be 40-50 odd end ahead with three wickets down is not a terrible position to be in. We’ve got to back ourselves to bat very well tomorrow.
“There is still a lot of time in the game. If one guy gets a hundred and it is backed up by people coming in next, a target of 250-300 will make it interesting coming into the last innings of the game.”
Worcestershire batsman Joe Clarke, on scoring his first century of the season, said: “It is a relief if anything really. I’ve struggled really.
“I’ve been wanting to get big scores all season and it hasn’t quite happened for me.
“I’ve been getting starts and not being able to go on. It was nice to go on past 20 or 30 and get a hundred.
“I’ve felt in good nick all year really. It’s just been one of those things. I’ve kept getting to 20 and 30 and giving it away.
“It’s been very frustrating and it’s a relief to go on and get a hundred.
“There is a bit in the pitch with the new ball. There is carry in it for the bowlers. It’s just once it get past 20 overs, it gets a bit slower and if you can get in, you can score runs.
“If we hit our areas tomorrow morning and get a couple of wickets, then we are right in it.”
Kent won the toss and elected to bat.
Kent side: Bell-Drummond, Dickson, Denly, Northeast, Weatherley, Stevens, Gidman, Rouse, Coles, Shah, Claydon.
Worcs side: Mitchell, D’Oliveira, Moeen Ali, Clarke, Rhodes, Cox, Whiteley, Barnard, Leach, Hastings, Tongue.
Close of play day two: Kent 260 all out & 120/3, Worcs 336 all out.