Glen Chapple finished with five for nine and Kyle Hogg ended with four for 11 after they produced a breathtaking spell of new-ball bowling.
The visitors had gained a first-innings lead after being bowled out for 398 with the last three wickets adding 190 runs including half-centuries for Hogg and Chapple before the pair made it a day to remember for both themselves and their team.
Pace bowlers Will Gidman and James Fuller ripped through some frail Hampshire batting to earn Gloucestershire their second win of the season inside three days at the Ageas Bowl.
In fact, with the first day washed out by rain, the match lasted only two days as Gloucestershire - after setting Hampshire 411 to win in 169 overs - won by 198 runs rather more easily than they could have anticipated.
Gidman's gentle medium pace earned him figures of four for 46 and Fuller took three for 54 as Hampshire failed to rise to the challenge.
Leicestershire's game against top-of-the-table Northamptonshire ended in a draw after rain reduced the final day's play at Grace Road to just 36.1 overs.
In that time Leicestershire advanced from 142 for three to 238 for six, leaving them 329 behind Northamptonshire's mammoth first-innings score of 567 for seven declared.
Finally, Glamorgan appeared to be homing in on their second win of the campaign after making basement side Kent follow on at Canterbury.
Dismissed for 135 to concede a first-innings lead of 243, winless Kent batted marginally better second time around to at least take the game into its final day by reaching 254 for four at stumps - a slender match lead of 11.