Skipper Steve James top-scored for the Dragons with 55 not out to ease past Durham's 161 all out with more than 10 overs to spare.
The visitors lost both openers within the first five overs, Ian Thomas was out hooking Mark Davies for eight, Nicky Peng taking the boundary catch, and pinch hitter Robert Croft departing for seven, caught at backward point by Gary Pratt off Neil Killeen.
However, the experienced Matthew Maynard (24) and Mike Powell (39) put on 54 for the third wicket to settle the visitors' nerves and despite losing wickets at regular intervals, they never really looked in danger of defeat.
Maynard was another out hooking, caught by Ian Hunter off Nicky Phillips, while Powell was run out by a direct hit from Phillips trying to nick a single.
Adrian Dale was then bowled second ball by Phillips without scoring, while Mark Wallace went for nine, edging Hunter to wicketkeeper Andrew Pratt.
Darren Thomas was caught and bowled by Killeen for seven, but despite a spirited bowling performance, the home batsmen had not given their bowlers a big enough target to defend, and former England man James calmly picked off the runs to see his side home.
Earlier Darren Thomas had taken three quick wickets to induce a spectacular collapse as Glamorgan bowled the Dynamos out in the 43rd over.
The hosts, having won the toss and elected to bat, were going well at 77 for one in the 19th over when opener Michael Gough, who had made 42, edged the Dragons medium pacer to wicket-keeper Wallace.
In his next over Thomas accounted for both Danny Law (15) and Gary Pratt (nought) and all of a sudden the Dynamos were 86 for four with two new batsmen at the crease.
Dean Cosker then had Ashley Thorpe caught at mid-wicket by Maynard for nine and two balls later the same fielder ran out Andrew Pratt for a duck trying to steal a single.
Maynard's starring role in the field continued when he took another catch at midwicket two overs later to send Ian Hunter packing for three off Croft's bowling.
With the wickets crashing around him, skipper Jonathan Lewis was Durham's last hope of posting a decent total, but he became the second man run out in the next over having scored 20, James doing the fielding this time.
The hosts had lost seven wickets for 44 runs and Phillips and Davies came together in the 30th over knowing they needed to at least see out the 45 overs.
They put on 22 before Mike Kasprowicz bowled Phillips off his pads for 13 and while last man Killeen struck a couple of useful boundaries off Croft, the England spinner got his revenge with an lbw decision in the 43rd over to dismiss the home paceman for 11.
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