After being promoted to the first-class ranks in 1992, their highest Championship finish is 16th in their first year. However, last week's one-wicket victory over Middlesex put them in third position, 21 points adrift of the leaders, Surrey.
Vice-captain John Morris is ruled out of today's match, but just five points will be enough to take Durham past second-placed Sussex, who are without a game in this round.
While Durham are flourishing, their neighbours, Yorkshire, are struggling with a series of injuries that has left them 44 points adrift of Surrey in eighth place, having led the table after the first two matches.
Already resigned to the loss of the main strike bowler, Darren Gough, for today's match against Hampshire at Headingley after he broke his finger on Test duty, they are now destined to be without the all-rounder Craig White and batsman Darren Lehmann after they both aggravated back problems in Tuesday's Benson and Hedges Cup semi-final defeat by Essex.
Without Gough and White, who is leading the first-class bowling averages, Yorkshire are forced to rely on the youngsters Gavin Hamilton, Ryan Sidebottom and Paul Hutchison to lead their attack.
Surrey, meanwhile, will aim to recover from their Benson and Hedges Cup semi-final defeat against Leicestershire when they take on Essex, but will be without Ian Salisbury, who injured his upper leg while bowling at Leicester.