Cameron Bancroft was out first ball for Gloucestershire, and there was an unusual dismissal for Ollie Price (36) who was bowled over his shoulder by an Andrew Neal full toss which was not a no-ball because he had got down so low at the crease.
Bracey, though, made 104 off just 84 balls and his score was matched by Charlesworth, who hit four sixes and eight fours, as they put on 118 in a score of 313-7 by the home side.
With Nick Gubbins setting the pace as the highest scorer in the competition, Hampshire were still in the hunt and he went past 650 runs in making 76 off 60 balls before being caught behind as he tried a reverse paddle sweep.
Gubbins put on 112 in 11 and a bit overs with Ali Orr (52), but it was Fletcha Middleton (92 off 95 balls) and Toby Albert (52) who carried them most of the way to their target before departing in the space of three overs and they eventually reached 315-5 from 47.4 overs to move above their opponents into second place.
It was a high-scoring game at Derby, with three batters making hundreds as Essex defeated the Falcons by 44 runs, with Martin Andersson unable to bat for the home side.
Captain Tom Westley put on 127 with Charlie Allison (64) and made 118 off 110 balls before being caught at mid-wicket off Rory Haydon, but Luc Benkenstein hammered a 38-ball 50 and his 75, including five sixes, propelled the total to 366-6.
Derbyshire lost Caleb Jewell early but Matthew Montgomery (108 off 91 balls) and Harry Came (139) shared 225 for the second wicket before the former was bowled by Simon Harmer (2-45).
Came was stumped off Matt Critchley and the innings gradually subsided and Derbyshire were all out for 322 in the 48th over.
In Cardiff, holders Glamorgan were eager to avoid being the only team not to win a group game and youngsters Tom Norton and Romano Franco each took three wickets as Leicestershire were all out for 274, Lewis Hill top scoring with 81.
Tribe, however, gave another demonstration of his quality, reaching 100 off 109 balls with a square cut for four off Roman Walker as he and Will Smale (83 not out off 89) powered them to 278-3 to win by seven wickets.