The Nottinghamshire skipper lost the toss but his bowlers restricted the hosts to 159 for six, with Andrew Gale contributing 50 runs to the total.
Fleming then struck 60 from 52 balls to get within sight of victory, supported by fellow opener Graeme Swann (32) and Samit Patel (43). David Hussey finished the job with an unbeaten 21.
Led by Adam Griffith, Leicestershire's bowlers restricted Derbyshire and recorded an 18-run victory at Grace Road.
The hosts reached 161 for six after a half-century from South African batsman HD Ackerman, giving Derbyshire hopes of a win to hoist them off the bottom of the North Division.
Griffith then took two for 27 from his four overs, with the visitors falling short despite 57 from Stephen Stubbings.
David Sales struck 62 off 40 balls as Northamptonshire beat Somerset by five wickets at Taunton.
Hosts Somerset set an imposing total of 188 for six, with Australia Test star Justin Langer falling three runs short of a century.
Robert White (37) and Usman Afzaal (33) got Northamptonshire off to a good start before Sales took over, helped by a quickfire 28 from South Africa all-rounder Lance Klusener.
In the day's other match between Glamorgan and Warwickshire in Cardiff, rain forced an abandonment.