Only a win over Sussex would give Gloucestershire a chance of continuing the defence of their title but David Payne could not defend 15 runs off the final over as Danny Lamb hit three fours to take the Sharks to victory.
D’Arcy Short’s 66 from 45 balls powered the home side’s innings, with Cameron Bancroft (45) and Ben Charlesworth (44) offering useful support as they made 185-5 on the small College Ground at Cheltenham.
Sussex’s reply got off to a rapid start before the loss of three wickets for 28 runs reduced them to 57-3 in the ninth over.
James Coles (62) and Tom Alsop (55) then looked to be guiding the Sharks to a comfortable victory but when Coles perished to a catch in the deep to end a 106-run partnership and Alsop was out soon after, the scales seemed to swing in the champions’ favour.
John Simpson was run out from the first ball of the final over but Payne then sent down a wide and a waist-high full toss which went for four before Short turned from hero to villain when dropping a simple chance offered by Lamb at long-off.
Lamb promptly smacked the final two balls for four to secure a four-wicket win and move Sussex up to fourth place to put them in pole position to sneak into the last eight.
“It just came down to a couple of key mistakes that probably made the difference in the end,” said Gloucestershire head coach Mark Alleyne.
“First of all, the umpire’s interpretation of a wide against David Payne in that final over is absolutely wrong.
“D’Arcy Short then missed that catch and we conceded two runs. It should have been a dot ball and it should have been our game.”
Hampshire must have fancied their chances of joining Surrey and Somerset in qualifying from the South Group as they piled up 220-6 against Essex but Cox had other plans as the Eagles produced a bright moment in what has otherwise been a miserable campaign.
Toby Albert’s 84 from 55 balls was the mainstay of the visitors’ mammoth total while Tom Prest (41) and Hilton Cartwright (56) also found the home bowling very much to their liking.
Essex skipper Simon Harmer used eight bowlers in an attempt to find a way of stemming the Hampshire run-fest with Scottish international Mackenzie Jones picking up 2-46 on his Blast debut.
With nine defeats from their 12 games, chasing 221 for victory seemed unlikely for the Eagles but Cox’s maiden Blast century took the game away as they got home with four balls to spare.
Cox hammered 11 fours and 11 sixes in his unbeaten 139 which is the highest score in this year’s competition.
Fourth-placed Sussex and fifth-placed Kent will battle it out for the final qualification place on Friday, with third-placed Hampshire, who have played all their games, all but there.