The win over the Foxes was their seventh in the competition this season and their most comprehensive.
The Welsh side now have to beat Yorkshire at Headingley in their final Group C match on Monday and hope other results go their way to make the last four.
In front of a big crowd, Glamorgan cracked 303 for six from their 40 overs with Chris Cooke top scoring with 85 from 76 balls. In reply Leicestershire could only make 235 for six with Niall O'Brien making 92.
For Glamorgan there were also useful contributions from Murray Goodwin, who struck 48 from 19 balls, including four sixes and Mark Wallace (50) and Gareth Rees (48).
The only Leicestershire bowler to emerge with credit was off spinner James Sykes, who claimed two for 37 from his eight overs.
Ravi Bopara warmed-up for the forthcoming one-day international series between England and Australia by scoring 88 as Essex beat Derbyshire by 107 runs in their Group B clash at Colchester.
Bopara's fine effort, from 87 balls, keeps Essex on course for a place in the semi-finals of the competition after they had totalled 259 for seven.
It was a target that always looked beyond the visitors, who fielded a weakened side, and lost their first four wickets before the fifty was raised before eventually subsiding to 152 all out in the 32nd over.
Essex left-arm seamer Tymal Mills took the wickets of openers Wes Durston and Chesney Hughes for single figure scores, with his pace proving too much for either batsman to handle.
Reece Topley (four for 26) and Tim Phillips (two for 20) then made steady inroads into the innings, but former Essex batsman Billy Godleman did spare Derbyshire from complete humiliation with a fighting 60 from 74 deliveries before becoming one of Topley's victims.
Godleman shared in a half-century stand with Alex Hughes, who made 28, before being bowled by Ryan ten Doeschate, but once that stand had been broken, the visitors folded quickly.
The last four wickets went down in as many overs as the innings came to an abrupt end.
Thanks mainly to the accuracy of Tony Palladino, Essex were restricted to 66 for two after 16 overs, having been put into bat by Derbyshire.
Former Essex fast bowler Palladino removed openers Gautam Gambhir and Mark Pettini for 21 and 23 respectively.
But Bopara and Greg Smith were to provide welcome momentum with a stand of 80 in 13 overs before the latter fell to Ally Evans for 30.
By this time, Bopara was moving through the gears and had struck six fours and three sixes when, within sight of his season's second century in the competition, he was trapped leg before by Alex Hughes.
It was late flourish by James Foster and Graham Napier that saw Essex to their imposing total. The pair put on 52 for only 23 balls, of which Napier collected 23 from just 10 deliveries before he was caught in the deep.
Foster departed in the same manner to the final ball of the innings, his 41 containing five fours and a six and arriving from 24 balls.