Captain Andrew Gale will demand a final day push from his bowlers as Yorkshire attempt to climb to the top of the LV= County Championship table.
England spinner Adil Rashid led the way with four for 73 as the Tykes forced Durham to follow-on at Headingley still 195 shy of their first innings total of 426 despite a gritty 64 not out from Paul Collingwood.
By the close, the visitors had reached 59 for one in their second innings, with Adam Lyth having accounted for opener Keaton Jennings, but 136 runs shy of making Yorkshire bat again.
Prospects of result at Uxbridge could depend on the weather with Middlesex heading into the final day of their showdown with Somerset holding a 243-run lead with eight second-innings wickets remaining.
Having declared on 264 for nine - still 74 runs behind - after Nick Compton went for 94, Somerset were boosted by the first-over departure of opener Chris Rogers, but found the going tough thereafter as the home side reached 169 for two by the close.
In Division Two, Surrey had bowlers Matthew Dunn and Arun Harinath to thank for paving the way for a nine-wicket victory over Glamorgan at Colwyn Bay which maintains the pressure on leaders Worcestershire.
Dunn's second innings haul of four for 124, aided by a return of two for two from part-time seamer Arun Harinath, helped to end the home side's brave resistance with their lead at just 41, and although opener Rory Burns went without scoring, Zafar Ansari and Harinath eased Surrey home - and into second place in the table - inside 13 overs.
Hampshire face a fight to hang onto their coat-tails after seeing number six Will Gidman score his first century of the season as Gloucestershire secured a 149-run lead to take into day four.
The visitors reached stumps at 446 for five at the Ageas Bowl with Gidman and Ian Cockbain putting on 161 for the fifth wicket to leave their side in control.
Opener Nick Browne became only the 10th Essex player to carry his bat as he claimed a maiden first-class century against Derbyshire at Chesterfield.
However, Browne's unbeaten 132, which contributed to a slim two-run first innings lead, counted for little as Shivnarine Chanderpaul hit 62 not out with Derbyshire finishing the day on 237 for five.
Bottom-of-the-table Leicestershire showed fighting spirit as a sixth-wicket stand of 175 between Josh Cobb and Rob Taylor enabled them to set Kent a victory target of 304.
Cobb's first century for two years - he went on to make 137 - and a career-best 98 from Taylor eased the home side towards a second innings total of 388, although Kent's response had reached 66 for one by stumps, meaning they need a further 238 to win.