Gloucestershire 368 (Bracey 63, Roderick 57, Dent 57, and 15 for 0 beat Leicestershire 222 (Cosgrove 92, Shaw 4-54) and 160 (Cosgove 68, Norwell 8-43) by 10 wickets
Liam Norwell took the final three wickets in Leicestershire's second innings to finish with a first-class career best return of 8 for 43 as Gloucestershire completed a ten-wicket victory at the Fischer County Ground.
His return was the best in Division Two of the County Championship this season, and also meant the young seamer had taken ten wickets in the match for the second time against Leicestershire this season.
"We made three changes for this match, with Matt Taylor, Josh Shaw and James Bracey coming in, and they all took their chance and made an important contribution to the victory," Richard Dawson, Gloucestershire's coach, said.
"We're still searching for the big partnerships of over 100, but we had three or four partnerships of 50-plus, and they helped us build a solid first innings score in difficult conditions. The challenge now is to take this form into our match against Kent at Bristol next week.
"Liam Norwell is a class act, there's not many better seamers around in county cricket at the moment."
With Leicestershire resuming on 152 for 7, leading by only eight runs, Gloucestershire's only real concern was the weather, but play started on time, and Norwell made an immediate breakthrough, with a delivery which Matt Pillans edged to George Hankins at third slip.
The end was not long coming as Clint McKay then edged an expansive drive to Gareth Roderick behind the stumps before Dieter Klein edged to Chris Dent at second slip.
Gloucestershire openers Dent and Cameron Bancroft needed just 3.3 overs to score the 15 runs needed for the visitors to complete their third victory of the season, and leave Leicestershire still winless after a hapless performance in which only captain Mark Cosgrove, who hit 170 of the 382 runs Leicestershire scored in the match.
"Obviously we haven't played our best game over the last four days, and today was another disappointing effort," Cosgrove said. "It was an opportunity to play good cricket which we didn't take, but the season's not over, there are two more games to show we're good cricketers, and we have to turn it around quickly.
"We'll look hard at selection, especially after a game like we've played here. It could be tough at Worcester, with Ashwin in the side they'll probably prepare a dry turning wicket, but we have to look at it as another opportunity to do well.
"It is a tough ask to lift players in these circumstances but we'll regroup and try and have a good lead-in to the game next week. We do need some positives going into the winter because otherwise it could be a very long pre-season for some of the boys."