Glamorgan 300 for 6 (Cooke 98, Allenby 85, Reed 5-31) beat Unicorns 215 for 9 (Park 74, Wagg 4-51) by 85 runs
A battling 74 from Garry Park was not enough to prevent the Unicorns from slumping to a sixth defeat in seven Yorkshire Bank 40 matches as Chris Cooke's 98 put Glamorgan out of reach at Southend.
Park's knock was the stand-out effort in the Unicorns' 215 for 9 but it proved in vain in response to the Welsh county's 300 for 6.
A surprise victory for the hosts never looked likely once an early onslaught subsided. Needing 7.5 runs per over from the outset, the Unicorns started with purpose but with Tom Lancefield and Michael O'Shea back in the pavilion with 30 on the board their momentum stalled.
Scott Elstone and Park put on 71 for the third wicket before the former departed two short of a second half-century of the season.
Vishal Tripathi and veteran skipper Keith Parsons failed to make much of an impression and the game was effectively over when Park was out after a 70-ball knock which included seven fours and a six. Graham Wagg swept through the tail to finish with figures of 4 for 51.
Glamorgan, who moved up to fourth in Group C with the win, received important contributions from opening pair William Bragg and Mark Wallace while Cooke and Jim Allenby built on the platform with some lusty hitting.
Bragg and Wallace put on 82 in just 69 balls for the opening wicket and although both were accounted for by Dominic Reed in relatively quick succession, the Unicorns bowlers were offered no let-up.
Former Australia Test batsman Marcus North made just 12 but that allowed Cooke and Allenby to come together. The pair bludgeoned 162 from 18.2 overs before Cooke was bowled by the excellent Reed as he approached three figures.
Allenby also perished to Reed, who finished with 5 for 31, for 85 after an entertaining knock which saw him hit four fours and six sixes.