Sam Northeast and Gareth Rees starred for Kent and Glamorgan respectively with the bat as their LV= County Championship Division Two clash appears set to end in a draw.
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Northeast notched 102 off 202 balls for his second ton of the championship season to help Kent to 329 at the end of their first innings.
But Rees finished the penultimate day 72 not out as Glamorgan reached 150 for three, with a lead of 92 runs, at stumps.
Glamorgan's rookie spinner Kieran Bull was the pick of the bowlers, claiming four for 62.
Kent, resuming on their overnight score of 205 for four and still trailing by 124 on first innings, saw their best hope of adding impetus into the game perish within 20 minutes when Darren Stevens departed for 30.
In aiming an uppercut over the slips against the second new ball, Stevens only succeeded in edging a third catch through to Glamorgan's keeper-captain Mark Wallace.
It proved Kent's only loss of the session as the hosts added 108 in the morning session once Northeast and Sam Billings joined forces.
The sixth-wicket partners both passed 50s - Northeast from 128 balls, Billings from only 86 balls and with six fours - as the duo edged Kent beyond the Glamorgan total soon after lunch.
They added 151 in 38.1 overs - Kent's second highest partnership of the championship summer - before Billings, on 77, slog-swept one from Bull into the hands of David Lloyd at deep mid-wicket to make it 369 for six.
With spin at both ends, Kent suddenly got into difficulty. Bull snared Mitch Claydon lbw in his next over then Northeast, having posted his century from 197 balls, with nine fours and a six, departed for 102.
Advancing down the pitch, the wily Dean Cosker saw him coming and dropped it short to have the Kent bat caught cutting at backward point.
The Welsh spin combo made light work of the tail thereafter, Bull claiming three for seven in 39 balls in his post-lunch stint to finish with four for 62 on his four-day bow. Cosker bagged two for 53 as Kent succumbed on the cusp of tea for 387, for a modest first innings lead of 58.
Kent's lengthy tail and its subsequent collapse sparked debate among home supporters as to whether their skipper, Rob Key, might have declared soon after passing 300.
In conceding a first innings deficit some pondered, the onus of setting a target and opening the game up would have been transferred onto the shoulders of Key's Glamorgan counterpart, Wallace.
Honour bound to set Kent some sort of a last-day target, a teasing target from Wallace may have provoked a Kent run chase, opening the game up on its final day and, with so little time left in the game, would have offered Glamorgan their sole chance of forcing victory.
Declaring in arrears might also have proved Key's best chance of clinching his side's outside chances of victory in this game, and with it, maintaining Kent's fading hopes of securing promotion. As it was, his side faced a long 40-over final session in the field and a battle to take another 10 Glamorgan wickets.
Kent's quest started spectacularly when Claydon broke Will Bragg's off stump in two with one that jagged back down the Nackington Road slope to make it seven for one.
Jacques Rudolph, propping half forward and outside the line of a Stevens' off-cutter, departed lbw with his side still 17 behind.
With 100 on the board and their noses 42 ahead, Glamorgan lost a third wicket when first innings century-maker Chris Cooke (30) edged behind when aiming a back foot punch against Robbie Joseph.
Gareth Rees held firm thereafter, scoring his first championship 50 since the last week in April from 91 balls and with six fours and a six.