The hosts won the toss in Cheltenham, putting Hampshire into bat, and were able to remove the visitors in 20 overs.
Hampshire put up just 116 from their 20 overs as Craig Miles led Gloucestershire's attack with three wickets.
James Vince was Hampshire's top scorer with 32, but no-one else scored more than 22 as the away side struggled to post a tough target to chase.
The visitors' hopes of snatching an unlikely victory were given a boost when they got rid of Michael Klinger in the first over, but Gloucestershire steadied themselves and always looked like reaching the victory target.
Jones's 40 off 30 balls led the way as Gloucestershire reached the required number with eight balls to spare.