Fleming, now also the Nottinghamshire skipper, was 223 not out at stumps. The left-hander struck five sixes and 27 fours in his near run-a-ball innings as the visitors ended a day disrupted by a wet outfield on 580 for four - a lead of 363 in reply to Surrey's 217.
Former Nottinghamshire Jason Gallian weighed in with 141 while Darren Bicknell, once a Surrey stalwart, scored 91 and David Hussey 74 as both teams looked to maintain their unbeaten start to the season.
Elsewhere Glamorgan were forced to follow-on against Gloucestershire at Sophia Gardens after all-rounder Alex Gidman broke through the hosts' top order with four for 47.
The hosts were bowled out for 239 in reply to Gloucestershire's 466 and at the close in their second innings were 93 for one - still 134 runs shy of making Chris Taylor's team bat again.
At the Rose Bowl, Middlesex eked out a first innings lead of four runs over Hampshire after being bowled out for 279, Owais Shah (83) and Ed Joyce (70) the main contributors.
But the home side also struggled before closing on 28 for two in their second innings, just 24 runs in front.
In the Second Division, Mal Loye and Australia's Brad Hodge guided Lancashire towards a first innings lead against Derbyshire on a rain-affected day at Old Trafford.
Lancashire, starting the day on 65 without loss, finished on 175 for one with Loye 91 not out and Hodge 24 not out after Mark Chilton made 50 to be 40 behind their opponents.
Australian seamer Damien Wright starred for Northamptonshire by taking eight for 60 as Yorkshire were bowled for 328 at Headingley.
The visitors were nine without loss in their second innings come Saturday's close, 38 runs behind Yorkshire.
Durham's lower order in the shape of Liam Plunkett (74 not out) and Mark Davies (62) rallied the tail to turn 141 for seven into 298 all out, a lead of 46 at Stockton.
Somerset ended on 88 for three, 42 in front, but with both England opener Marcus Trescothick and Sri Lanka's Sanath Jayasuriya, arguably an even more dangerous left-hander, both back in the pavilion.
Essex's Will Jefferson, at some 6ft 10" the tallest player in the County game, fell seven run short of a hundred but did enough to put his side on top against Leicestershire.
The opener was the only Essex player to reach a half-century in their first-innings 362.
Leicestershire, 57 for one, in their second innings, trailed by 85 runs.