Gloucestershire 80 for 0 dec and 307 for 9 (Roderick 152*) need another 92 runs to beat Kent 474 and 4 for 0 dec
A dogged career-best 152 not out by Gloucestershire's rookie wicketkeeper Gareth Roderick thwarted Kent's hopes of securing a three-day win in Canterbury.
The 21-year-old South African dug in for five hours to deny the hosts the chance of completing a second division double with a day to spare as the visitors limped in at stumps on 307 for 9 - trailing by 91 runs but with only one second innings wicket intact.
Though Kent claimed the extra half-hour in a bid to wrap up the their second win of the season, Roderick held firm to give his side an outside chance of securing a draw should the forecast rain arrive in the south-east on the final day.
In pursuit of 399 for a fourth championship win of the campaign, promotion-chasing Gloucestershire lost captain Michael Klinger as early as the fifth over.
In attempting a flashing cover drive, he edged a Charlie Shreck leg-cutter to slip, then Benny Howell, promoted to bat at No. 3, went without scoring after spooning a low catch to Sam Northeast at cover.
Gloucestershire slid even deeper into the mire when left-handed opener Chris Dent, having played one scoring shot in 36 minutes, followed one going across his body from Calum Haggett to edge to the wicketkeeper and make it 13 for 3.
Alex Gidman and Hamish Marshall steadied the ship, albeit temporarily, in adding 28 before Marshall edged a leg-glance against Mitch Claydon to give keeper Geraint Jones a second catch of the session. Gidman and Gareth Roderick added 55 in 14 overs either side of lunch until Gidman, on 47, edged a delivery to first slip to give the impressively obdurate Haggett a deserved second scalp.
Will Gidman departed soon after when his leg-side flick against Darren Stevens feathered the inside edge through to the keeper, bringing together Tom Smith and Roderick for a seventh wicket stand worth 109 in 33.3 overs.
Roderick celebrated his maiden Championship ton from 157 balls and with 14 fours but lost Smith to the fourth delivery bowled with the second new ball when he pushed at one from Shreck to give Jones the fourth of his five catches.
David Payne went in identical fashion to an even better diving catch by Jones then, five overs into the extra half-hour, James Tredwell turned one through the gate of Craig Miles to peg back offstump and make it 299 for 9.
The day started with the drama of two quickfire declarations after the captains, presumably with one eye on the miserable weather forecast for Saturday, contrived a third-day run chase deal. For his part Gloucestershire skipper Klinger declared on his side's overnight total of 80 without loss - a match deficit of 394 runs on first innings.
Kent then batted for four minutes, enabling the visitors to make good their poor over-rate and for Kent to add four runs before Kent captain Tredwell declared, leaving the visitors with almost six full sessions to score at an asking rate of 2.1 an over for victory.