Gloucestershire 241 for 4 (Hankins 67, J Taylor 64) beat Sussex 240 (Wright 84, Evans 48, Liddle 5-52) by six wickets
Jack Taylor's fourth half-century in this season's Royal London One-Day Cup steered Gloucestershire to a six-wicket win with eight balls to spare at Eastbourne and dented Sussex's hopes of reaching the knockout stages.
Chasing 241 for victory, Gloucestershire needed 98 off 13 overs when Taylor came to the crease but, with wickets in hand, he was able to go on the attack straight away.
Taylor hit three leg-side sixes and seven fours in an uncomplicated exhibition of clean hitting, although he was dropped on 54 and 62 when Stiaan van Zyl and substitute fielder Delray Rawlins shelled straightforward catches in the deep.
Taylor was eventually yorked by Jofra Archer for a List-A best 64 from 36 balls but Gloucestershire secured victory off the next delivery.
Ian Cockbain gave Taylor good support with 45 not out in a stand of 97 in 11 overs after skipper Michael Klinger and George Hankins had laid the foundations for their side's third win in the South Group by putting on 96 in 25 overs after Phil Mustard had been bowled by Archer in the seventh over.
Both batsmen were victims of Will Beer and the leg-spinner and slow left-armer Danny Briggs were tough to get away on a slow, low surface.
But Sussex suffered a blow when skipper Luke Wright had to go off with a hand injury when he put down a difficult low chance to his left at mid-on trying to intercept Klinger's powerfully-struck drive.
Having dropped out of the top three in the South Group, Sussex now need to beat Hampshire at the Ageas Bowl on Wednesday to have a chance of reaching the knockout stages.
Sussex were playing their first game at Eastbourne for 17 years and the crowd of 3,500 were anticipating a home victory when they reached 169 for 3 in the 35th over after Wright and Laurie Evans had put on 102 in 21 overs for the fourth wicket.
Wright and Evans had taken 33 runs from the previous four overs but Chris Liddle returned for a second spell and immediately had Evans caught off a mistimed pull on the midwicket boundary for 48, which included two leg-side sixes.
His dismissal prompted a steady decline in the innings as Sussex lost their last seven wickets for 71 runs in 15 overs.
Wright, increasingly bogged down by the accuracy of Gloucestershire spinners Tom Smith and Graeme van Buuren, was next to go to a catch at the wicket for 84, trying to force the pace against Liddle.
There was little to commend Sussex's lower-order batting with the exception of Archer, who hit two sixes onto an adjacent croquet lawn in 30 from 25 balls before he drilled a return catch to Benny Howell off the penultimate ball.
Liddle finished with 5 for 52 against his former county and has now taken 18 wickets in this season's competition while Van Buuren and Eastbourne-born Smith exploited the slow turn, with Smith finishing with 3 for 33.