The visitors resumed 153 behind, on 213 for four, and lost overnight duo Michael Powell and Mark Wallace in successive balls.
Glamorgan skipper Robert Croft together with Darren Thomas held Warwickshire up but could not prevent a resounding defeat.
Warwickshire and England left-arm spinner Ashley Giles took three for 85.
Elsewhere in the top flight, Hampshire captain Shane Warne oversaw the southern County's 48-run victory against Gloucestershire at the Rose Bowl.
But it was not the Australian leg-spin great who did the damage on the last day but former Sussex seamer Billy Taylor who took a career best six for 45 as the visitors were bowled out for 203.
In a rain-affected draw at The Oval, several Surrey batsmen made runs against Sussex with captain and ex-England batsman Mark Ramprakash leading the way with 152.
Alistair Brown (74 not out) wicketkeeper Jon Batty (70) and current Test batsman Graham Thorpe (59) were also in the runs as the hosts made 402 for five declared in reply to Sussex's 370.
In the Second Division, Worcestershire thrashed cash-strapped Derbyshire by 10 wickets with England off-spinner Gareth Batty taking five for 87 as the hosts were bowled out for 285. That left Worcestershire needing 71 to win and they knocked off the runs with ease.
Another rain-affected match saw Lancashire, relegated from the top division last season, draw with Somerset at Old Trafford.
Lancashire batsman Mal Loye made 92 as the hosts declared on 195 for five, 246 ahead at tea, before bad light ended play with 10 overs left.
Yorkshire avoided defeat at Chelmsford after being bowled out for 205 in reply to Essex's 401 for four declared.
Following on the Tykes saw Australian batsman Phil Jaques score 67 not out in a total of 105 for two to secure the draw.