The only half-century of the match came from Nadeem Shahid with 58 but several of his team-mates chipped in with useful, if modest, knocks.
Five of the six Surrey bowlers took wickets, with Martin Bicknell's three the most, and the Hollioake brothers, Adam and Ben, finished off the innings with three between them.
The chasing pack are bunching up as they enter the final month in pursuit of Surrey and Northamptonshire. With the joint second-placed Yorkshire not playing, Warwickshire and Nottinghamshire took the opportunity to move up the table with decisive victories.
Gladstone Small took 4 for 14 for Warwickshire as they bowled out Durham for their lowest score in the competition.
An 88-run victory was signposted by Shaun Pollock's 56 off 55 balls as Warwickshire reached 187 for 8, and then settled by the bottom county's collapse for 99.
It was a sad introduction to captaincy for Simon Brown, leading Durham in the absence of Mike Roseberry who was resting because of a recently broken finger.
Pollock organised a big recovery with his side on 118 for 6 with the last 10 overs producing 67 runs.
Durham's openers quickly fell to Trevor Penney's brilliance in the field. Stewart Hutton was caught at backward point off Pollock and Sherwin Campbell was run out by a direct throw from the same position.
Boiling (27) survived three chances in becoming the only Durham player to score more than 20, but was then the first of two victims in successive deliveries from Small.
Nottinghamshire's move upwards came thanks to a nine-wicket win against Middlesex at Trent Bridge in a match reduced to 32 overs per side. Chris Cairns took 4 for 22 as the visitors lost their last six wickets for 29 runs.
Nottinghamshire's chase of 138 was a formality with Tim Robinson unbeaten on 66 off 88 balls, including five fours. He shared an opening stand of 83 with Mathew Dowman and then an unbroken partnership of 56 with Paul Johnson to see his side home.Reuse content