Northamptonshire finished day three on 149-4, still 216 behind, after being asked to follow-on by Yorkshire.
Bowled out for 94 in their first innings, newly-promoted Northants went back in trailing by 365 but - led by James Middlebrook's 63 - produced an improved showing on a day shortened to 49 overs by inclement weather.
Opener Middlebrook, born in Leeds and who started his career with his native county, became former Northants seamer Jack Brooks' seventh wicket of the match late on to ensure Yorkshire remain on course to complete victory barring more poor weather on the final day.
Brooks, who took 5-36 the previous day, also accounted Matthew Spriegel (7) after Ryan Sidebottom (2-31) earlier had both Stephen Peters (39) and Kyle Coetzer (39) caught behind.
At Old Trafford, Lancashire enjoyed the better of the 25.4 overs possible against Warwickshire on day three.
James Anderson (1-85) bowled last man Oliver Hannon-Dalby to finish off Warwickshire's first innings at 324 and limit the visitors' lead to 77.
Openers Paul Horton (27no) and Luis Reece (9no) survived a testing examination in early evening to guide Lancashire to 46-0 in their second innings at the close, still 31 behind.
There was no play at Chester-le-Street due to rain and bad light. Defending champions Durham go into the final day on 152-7 in their second innings, leading Somerset by 275.