The hosts started their innings well posting 48 in the first five overs.
Gareth Breese broke the opening partnership of 88 in his first over (11th) with Wes Durston caught behind for 25.
He struck again in his next over sending Martin Guptill (60) back to the pavilion after he miscued to Dale Benkenstein at extra cover which saw the Falcons at 103-2 with nine overs to go of their innings.
Breese featured in the third wicket too, running in from the rope to catch Chris Hughes (23), giving Graham Onions his only scalp of the innings.
Derbyshire ended their innings with 183 on the board.
The Dynamos opening pair started well, despite the light drizzle that began to fall after the first few overs, keeping ahead of D/L and the rate at which Derby scored in the earlier innings
A thirty ball fifty from Gordon Muchall, which included six boundaries, helped maintain the Dynamos momentum but with rain falling the pressure to keep ahead of any potential reliance on D/L should rain stop play saw Mustard stumped off Hughes for 36 off the first delivery of the 11th over.
Ian Blackwell joined Muchall with the total at 88-1 and added eight to the total before he was caught in the deep by Garry Park in the 14th over.
Wes Durston struck with the first and penultimate delivery of the 15th over as the Dynamos reached 117-4, with both Muchall (62) and Collingwood (6) caught by Knight and Clare respectively trying to boost the total with big hits over the boundary.
A late surge from Dale Benkenstein, who scored 19 off 9 balls, ended when he was caught on the boundary by Groenewald off Jones which left the Dynamos at 153-5, requiring 31 runs from the final two overs.
David Miller and Breese hit six boundaries and a maximum from their 24 deliveries which saw the Dynamos requiring 12 runs from the final four deliveries.
Despite the best efforts in the middle Derby fielded well to secure the win by just five runs.
Durham Dynamos take on Derby Falcons at Emirates Durham ICG on Sunday 12 June, 2.30pm start. Tickets are available to purchase on the gate from 12.30pm priced at £17.50 for adults and £6 for juniors.