Yorkshire were asked to follow on at Scarborough after losing their last seven first-innings wickets for just 63 runs this morning, having begun the penultimate day on 182 for three in response to the visitors' 573.
The home side then lost Adam Lyth cheaply in their second innings and at that stage Durham looked overwhelming favourites to claim a potentially key victory.
However, former Australia Test player Phil Jaques (151 not out) and New Zealand international Kane Williamson (90no) joined forces to put Yorkshire back into the game with a brilliant unbroken 257-run stand.
That left the pacesetters on 276 for one at the close, trailing by only 23 runs.
At Edgbaston, third-placed Sussex were 148 for three in their second innings, leading Warwickshire by only 65 runs at stumps on day three.
Warwickshire had earlier progressed from their overnight 252 for six to 394 all out with Jeetan Patel finishing unbeaten on 78. Patel then sent back Sussex openers Luke Wells (46) and Chris Nash (27) to leave his side in the box seat.
Somerset boosted their hopes of avoiding relegation after wrapping up an emphatic innings and 179-run win over fourth-placed Middlesex.
Having made Middlesex follow on 343 runs in arrears on Thursday, Somerset skittled their hosts for 164 second time around to wrap up their first win in four-day cricket at Lord's since 1983.
That saw Somerset climb out of the relegation places, leaving Derbyshire and Surrey occupying the bottom two spots.
Those two sides were facing each other at the Kia Oval, where Derbyshire closed the second day on 13 without loss in their second innings - trailing by 57 runs.
Surrey had earlier suffered a collapse after being reduced from 217 for four to 289 all out - including losing their last four wickets for just two runs - with Mark Footitt (four for 50) and David Wainwright (three for 46) doing the bulk of the damage.
In Division Two, leaders Lancashire were looking good value to beat Hampshire after second-placed Northamptonshire kept up the pressure with a big win over Glamorgan.
Lancashire set Hampshire a massive target of 496 to win at Southport after declaring on 284 for five in their first innings, openers Paul Horton (111) and Luis Reece (65) setting the foundations with a stand of 166.
The home side then reduced Hampshire to 137 for seven in their run chase, needing just three more wickets on the final day to take the win.
Northants already have their victory sewn up after thrashing Glamorgan by an innings and 25 runs inside three days.
Starting their second innings 212 runs behind, Glamorgan were bowled out for 187 with Azharullah and Trent Copeland each taking three wickets.
Gautam Gambhir's first century for Essex helped put his side in total control against Gloucestershire.
Gambhir scored 106 and opening partner Jaik Mickleburgh added 86 as Essex declared on 285 for four to set Gloucestershire a target of 432 to win at Bristol.
The home side closed on 19 without loss.
At Grace Road, Leicestershire were 190 for six in their second innings - leading Worcestershire by 126 runs heading into the final day.
Worcestershire were bowled out for 338 with Thilan Samaraweera scoring an unbeaten 144 before Leicestershire's first-innings centurion Ned Eckersley shone again with an unbeaten 91 as he fought to earn his side a defendable total.