Warwicks welcome back Neil Carter from injury for this Pro40 game which Warwicks needed to win after the defeat to Nottinghamshire, in order to make the semi-finals next month.
Warwicks were put into bat by Durham and Neil Carter and Varun Chopra started well. Carter hit seven fours from 30 balls before he was out for 35, bowled by Clayton.
Chopra continued to make runs, putting on 63 for the second wicket which saw Darren Maddy who had made 27, trapped lbw by Breese.
Chopra was finally out for seventy, caught by Coetzer to see Warwicks on 155-3.
Jim Troughton who finished not out on 48 and Clarke added another 53 for the fourth wicket and although there was a mini-slump, Warwicks ended their forty overs on 243-8.
In the third over of Durham's innings, Warwicks got the break through when Stoneman who had hit three fours was out for 13 after giving a catch to Rikki Clarke off the bowling of Neil Carter.
Phil Mustard and Ben Harmison put on 114 for the second wicket before the latter was caught by Westwood to give Chris Woakes a wicket.
Eighteen runs later, Woakes had his second wicket when Mustard was out for 90 from 72 balls including ten fours and a six and Ant Botha and Boyd Rankin both took wickets but Muchall and Coetzer steered Durham to victory.
On Wednesday, Warwickshire are in County Championship action with a home game against Essex at Edgbaston.