Durham are 25.5 points behind their neighbours with a game in hand after bagging 23, one short of the maximum, against hapless Surrey who took only two points from the match and remain bottom of Division One. The match against Yorkshire begins on Wednesday.
Not even a dashing innings of 89 by the world's best batsman, Hashim Amla, could save them from suffering a heavy defeat at Chester-le-Street for the second successive year.
Once Amla had gone 20 minutes before lunch the rest swiftly followed, with Mark Wood taking three wickets in four balls either side of the interval on his way to career-best figures of five for 44.
Five successive batsmen fell to catches by wicketkeeper Phil Mustard as Surrey succumbed for 169 after following on 313 behind.
Meanwhile, Lancashire moved closer to locking down the Division Two title by wrapping up a nine-wicket victory over Worcestershire at New Road.
A fifth win in the last six games has put Glen Chapple's table-topping team 34 points clear of Northamptonshire and 65 ahead of Essex, having played a game more than the third-placed county.
Although Worcestershire began the last day only 12 runs ahead with five wickets standing, they did their best to delay the Lancashire bandwagon before bowing to the inevitable.
After resuming at 166 for five, the home side finally capitulated for 241 and Lancashire cleared off their target of 88 with more than half a day to spare.