Glamorgan 186 and 33 for 4 trail Kent 436 (Crawley 168, Billings 85) by 217 runs
Kent opener Zak Crawley hit a fluent maiden first-class century to bolster his side's promotion hopes and leave them in total command of their Specsavers County Championship clash with Division Two basement side Glamorgan.
Crawley, the 20-year-old right-hander, hit a career-best 168 in a total of 436 as Kent posted a first innings lead of 250 before leaving the visitors to bat out the final hour of day two.
The visitors lost both openers Nick Selman and Stephen Cook, caught in the slips off Darren Stevens' away-swingers within six overs. Kiran Carlson toe-ended a Joe Denly long-hop onto off stump and, in the final over of the day, night watchman Kieran Bull, fended one from Matt Henry to first slip.
Wobbling on 33 for 4 at the close, Glamorgan will need a further 217 to make Kent bat again, but the day had belonged to Crawley.
In only his 20th first-class appearance Crawley, who honed his batting on 'The Head', the 1st XI ground at Tonbridge School - the alma mater of Colin Cowdrey and, more latterly, Ed Smith, England's national selector - Crawley played a four-hour innings crammed with top-handed cover drives that would have delighted Lord Cowdrey himself.
"It feels very good to be stood here tonight with a first hundred to my name," he said. "I've been waiting a while for it and have got out in the 90s a couple of times along the way, so to get over the line today was nice, but I was even more pleased to kick on afterwards.
"I'm not usually one for getting nervous in the 90s because I always believed 99 was as good as a hundred, but I'll admit I was nervous today. A couple of old memories started creeping in about getting out on 93 and 96 before, but once I got the all important single I was fine.
Batting in tandem with Sam Billings, Crawley helped add 132 in 29 overs for the sixth wicket as Kent set about firstly reaching Glamorgan's first innings of 186 and building a game-defining lead thereafter.
Resuming on their overnight score of 93 for 2, Kent suffered their first loss in the eighth over when Harry Podmore, their night watchman, fell for 2 - the second of four Kent players to be caught behind when leg glancing. Heino Kuhn fell in similar fashion soon after, flicking airily against Ruaidhri Smith to be caught by Cooke.
Crawley reached the 90s with a hooked six off Smith and went on to post his maiden ton in a shade over three hours, having hit 15 boundaries and faced 141 balls.
Daniel Bell-Drummond went soon after, pushing half forward with low hands, the England Lions batsman gloved a catch to second slip to send Kent into lunch with a slender lead of four runs.
The hosts pressed on after the resumption as Crawley plundered 24 boundaries, while Billings recorded his second half-century of a run-parched summer from 74 balls and with six fours.
It took a very good delivery from Bull to finally dislodge Crawley, the only casualty of the mid-session, after 304 minutes at the crease. Prodding forward to his 237th ball, Crawley was deceived by the off-spinner's flight and dip and a delivery that turned through the gate to clip middle stump.
A short, sharp shower rushed the players off for an early tea just before 3pm, after which, Ollie Robinson fell for 17 on his home debut, once again caught down the leg side when glancing.
Having battled away for three hours in posting 85 for his highest score since his last championship century against Gloucestershire in Bristol in August 2016, Billings fell to the first ball of a new spell from Michael Hogan. Pushed onto the back-foot by a 'hit-the-deck' delivery, the Kent captain was powerless to stop a shooting Hogan off-cutter from plucking out middle stump.
Having past the career milestone of 15,000 first-class runs, Stevens perished for 30 when driving a Jeremy Lawlor away-swinger to extra cover, leaving Grant Stewart and Matt Henry to take the home score beyond 400.
Having scored only two batting bonus points in their six previous home games, Kent notched five and a maximum eight bonus points in a match for the first time in 2018 before Henry holed out for 31 to leave Glamorgan to bat the remaining 14 overs of the day.