Maiden one-day centuries from Alastair Cook and Ian Bell led England to 288-2 off 50 overs after they were put in, with Bell 126 not out from 118 balls.
Bell and Panesar combined to run out Yuvraj for 45 off 39 balls when Zaheer sent him back and Panesar then bowled the tail-ender comprehensively before Anderson cleaned up Patel to put the seal on a highly impressive victory.
Paul Collingwood drove loosely to gully and the departure of Bell, who got an inside edge that left his off-stump out of the ground in the first over after tea, saw the scoring rate dip alarmingly.
And, although there were minor alarms when Bell was caught behind off Dalrymple's first ball and Trott was run out by the newly-arrived Tim Ambrose, Glamorgan's third Twenty20 defeat in four games was already pretty much cut and dried.
Debutant Vikram Singh was dropped on nought off Blackwell, Bell inexplicably spilling a chance that went straight in and out of his hands on the boundary.