Glamorgan 239 (Ingram 82, Coad 4-55, Fisher 4-55) and 141 for 7 (Tribe 50*, Coad 4-30) need 255 runs to beat Yorkshire 361 ((Hill 90, Wharton 63, Bess 50, Govin 4-67) and 273 (Bean 57, Lyth 55, Harris 5-73) lead by 238 runs
Yorkshire need three Glamorgan wickets to secure victory on the final day and remain in pole position to earn promotion along with already promoted Sussex.
The Welsh County ended the day 141 for 7, 254 behind, Yorkshire opening bowler Ben Coad picking up his 50th wicket of the season as he finished with 4 for 30.
Glamorgan had managed to bowl Yorkshire out for 273, James Harris taking his 600th first class wicket on the way to 5 for 73. Jersey international Asa Tribe was the only Glamorgan batter to hold firm with an unbeaten maiden first class half-century.
That still set the improbable target of 396 for Glamorgan to win and Yorkshire will feel confident of wrapping up victory given the way wickets have fallen in every morning session of this match.
Once again the morning conditions were helpful to the bowlers and Jamie Harris and Andy Gorvin were determined to take advantage, Harris getting Finlay Bean lbw in the first over and Gorvin clean bowling nightwatcher Matthew Fisher with an off cutter.
Harris was working on the basis that if the batter missed he either hit or appealed for lbw, it was the latter form of dismissal for both James Wharton and Jonny Bairstow.
Timm van der Gugten got in on the act, clean bowling George Hill, until a partnership between captain Jonathan Tattersall and Dom Bess settled nerves.
Both got into the forties and the lead climbed closer towards 400, before Tattersall was lbw to Ben Morris to give the Abergavenny debutant his opening first class wicket.
Van der Gugten removed Jordan Thompson lbw, the eighth wicket in a row to have been bowled or pinned in front, before they finally achieved a different form of dismissal when keeper Chris Cooke caught Bess, again off van der Gugten.
Harris returned to claim the wicket of Dan Moriarty and complete his five wicket haul, another clean bowled.
That mountain of chasing 396 to win got a little higher after the opening overs as they lost their two highest run scorers this season, Sam Northeast and Colin Ingram.
Northeast was lbw to Ben Coad in the first over of their reply, while Ingram set about the bowling in typically positive style before chipping one to midwicket, Coad again the bowler and James Wharton taking the catch, for Coad's 50th wicket of the season.
Kiran Carlson would have wanted to get into form ahead of Sunday's One Day Cup final against Somerset at Trent Bridge, following his golden duck in the first innings.
Tribe is in his second first class match and this was comfortably his best score as he held the innings together.
An excellent leg cutter from Coad that hit the top of off made the breakthrough as Carlson departed for 41. He was soon followed by Ben Kellaway and Cooke, both also falling to Coad, before Matthew Fisher bowled van der Gugten.
A brilliant one-handed diving catch by Finlay Bean saw the end of Mason Crane off the bowling of Jordan Thompson.