Leicestershire's off-spinner, Tim Mason, took a career-best 4 for 12 as Essex lost their last six wickets for 15 runs in six overs.
Paul Prichard and Stuart Law looked to have put them on the way to victory with an opening stand of 45 in seven overs but, when Prichard was bowled by James Ormond and Law was caught at deep midwicket off Phil Simmons, Essex capitulated.
Mason, who had taken only three wickets in his previous eight games this season, took two in two balls when he removed Paul Grayson and Stephen Peters and then Dominic Williamson trapped Danny Law lbw.
Mason claimed his third wicket when Mark Ilott was snapped up at slip by Simmons. Barry Hyam fell lbw to Williamson before Mason wrapped up the innings with the wicket of Peter Such as, for the second week in a row, Leicestershire bowled out the opposition for less than 100.
In the Leicestershire innings Ben Smith and Simmons both hit half-centuries and shared a fourth wicket stand of 94 in 15 overs.
The victory guaranteed Leicestershire a top-four finish and a share of the prize money.
Glamorgan claimed their sixth win in their last eight AXA League matches with a 56-run success against Derbyshire at Cardiff.
The visitors, set 211 to win, were unable to recover from the early loss of Michael Slater and Adrian Rollins and were restricted to 154 for 9.
Dominic Cork and Kim Barnett added 45 in eight overs for the third wicket but when Cork gave Adrian Dale the charge and was stumped for 15 Glamorgan quickly regained the initiative.
When Dean Cosker held a return catch offered by Barnett for the first of three wickets Derbyshire had little left despite a bright and breezy stand of 36 for the last wicket between Vince Clarke and Kevin Dean.
Cosker finished with 3 for 39 from his eight overs and Dale took 3 for 36. It was a fine all-round performance by Dale as Glamorgan's total owed much to his fourth-wicket partnership of 112 with Michael Powell.
Dale managed only three fours in reaching his half century off 72 balls and went on to pass his previous Sunday best of 67, also against Derbyshire but as long ago as 1987, finishing with 82.
Powell hoisted Blackwell over mid-wicket for the only six of the innings and also hit two fives in reaching his Sunday-best of 55.Reuse content