Durham elected to bat first and got off to a great start with openers Phil Mustard and Gordon Muchall finding the boundary in regular intervals before their partnership of 44 was broken when Mustard was caught at point by Wayne White off the bowling of Harry Gurney for 25.
Ian Blackwell joined Muchall from the crease and crashed three fours and one huge six off Foxes spinner Claude Henderson in his brief innings of 25 off 11 balls before he was clean bowled by Australian Andrew McDonald.
South African David Miller and Muchall then formed a useful partnership of 27 to take the Dynamos over the 100 run mark but this stand was ended by former England bowler Matthew Hoggard bowled Miller for 18.
Captain Dale Benkenstein continued the Durham onslaught along with Muchall as the Dynamos raced along at a rate of nearly nine an over for the majority of the innings.
Some great hitting from the skipper including a big six off Hoggard saw the Dynamos move past 150 however the Foxes captain soon got his revenge on his Durham counter-part by having him caught on the boundary by Henderson for 23.
Muchall was playing a steady knock as he held the innings together and he made his 50 off just 43 balls as the Dynamos looked to get above the 180 mark.
The opener was finally out in the last over of the innings going for one big shot too many as he was caught on the boundary by White off the bowling of Gurney for a great knock of 64 off 50 deliveries which included eight boundaries.
Gareth Breese and Liam Plunkett added two more runs before the end of the 20th over as the Dynamos posted a competitive total of 187-5.
The Foxes lost two early wickets in response with both McDonald (1) Cobb (17) falling to Mitchell Claydon as they fell to 22-2 after just two overs.
The visitors raced to 113-2 after ten overs but, with the partnership increasing in confidence, Benkenstein broke the stand when he had Jefferson trapped lbw on 63, a wicket that initiated a further flurry of success for the Dynamos attack with Plunkett subsequently picking up two scalps, those of Du Toit (33) who was caught by Miller and Razzaq who was caught by Breese having added just six to the score.
Benkenstein further slowed Leicestershire’s momentum when he claimed a second wicket when he bowled Nixon for 13 and with three overs to go the Foxes required 29 runs to sneak the win.
With an over to go they needed 13 to win but Claydon kept the batsmen at bay to ensure a Durham victory by three runs.
The Dynamos are currently third in the northern table.