Gloucestershire's batsmen made hay in the Bristol sunshine to inflict Leicestershire's third defeat in as many National League Division One games this season.
Philip Weston (92), Craig Spearman (89) and Tim Hancock (82) were the main contributors to a 45-over total of 311-4, the highest score Gloucestershire have ever made in the competition at their County Ground.
Leicestershire' were bowled out for 254 to go down by 57 runs, despite a sparkling 90 off 64 balls from skipper Phil DeFreitas and 65 from Darren Stevens.
Spearman dominated an opening stand of 139, but was then upstaged by Hancock who raced to 50 off just 34 balls.
He took a heavy toll on Jeremy Snape when his former team-mate was introduced as eighth bowler by DeFreitas.
Snape was taken off again after conceding 21 from two overs, 12 of them in the space of three balls as Hancock effortlessly lifted him over square leg for his third and fourth six.
Hancock had faced only 57 balls and hit six sixes and three fours when he became the third player to miss out on a century, bowled by Charlie Dagnall trying an ugly swing to leg.
Leicestershire were never in contention to reach their target after Jon Lewis took two early wickets, despite Stevens' 48-ball half-century, and some fine blows by DeFreitas in a seventh wicket stand of 110 with Snape.
By the time DeFreitas cut loose the runs per over required were in double figures. But he made Gloucestershire work for their win, hammering four sixes and eight fours.
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