In a match billed as must-win for both lowly placed teams, the hosts posted 242 for eight after losing the toss, Michael Klinger contributing 46 and Smith 43 not out. Chris Jordan claimed three for 55 and leg-spinner Will Beer two for 38.
In reply the Sharks could manage only 191 all out, despite an excellent unbeaten 87 from 21-year-old Harry Finch, left-arm spinner Smith taking four for 26 from his ten overs.
The result took the holders to four points from five games, while Sussex remain on just two.
Sussex top scorer Finch said: “We are very disappointed. At the halfway stage we felt we had bowled and fielded really well to restrict them to 20 or 30 below par.
“It wasn’t easy in the middle overs because the ball was turning and sticking in the pitch for their seamers. From 59 for four it was always going to be difficult.
“I have been happy with my form all season and feel I am playing well at the moment. As a team we aren’t far off, but it is clearly going to be hard to qualify now. We just have to treat our last three group matches as cup finals, win them all and see what happens.”
Gloucestershire lost wickets too regularly to ever gain much momentum to their innings. Chris Dent had already been dropped when falling early on for ten and it was 49 for two when Ian Cockbain was caught behind for eight in the ninth over.
Hamish Marshall’s disappointing last Cheltenham Festival ended when he was bowled off inside edge by Jordan for 11 before Beer struck a major blow in the 22nd over.
Klinger had looked in prime form moving to 46 off 66 balls, with 6 fours, when adjudged lbw pushing forward. It may have been a case of the ball striking pad before bat, but the Gloucestershire captain was clearly unhappy with the decision.
Beer also removed Benny Howell for 19 and when Graeme van Buuren was bowled by Jordan for 38 off another inside edge Gloucestershire were becalmed on 155 for six in the 35th over.
Kieran Noema-Barnett (29) hit the only six of the innings over mid-wicket off Danny Briggis, but it was Smith who did most to bolster the modest total, facing 46 balls and hitting 3 fours.
Young wicketkeeper Patrick Grieshaber contributed a bright 20 at the death, but Gloucestershire looked to be short of a par score.
Soon, however, the home bowlers were striking back. Ed Joyce mistimed a back-foot shot to be caught at mid-wicket off Matt Taylor and when Craig Miles had Philip Salt caught behind it was 19 for two.
Dangerman Luke Wright played a poor shot off Taylor on 18, chipping a catch to mid-on and Gloucestershire were right in the game at 43 for three in the ninth over.
Chris Nash was bowled off a bottom edge by Smith for six, but Finch and Ben Brown than gave Sussex hope with a stand of 70 in 19.4 overs before Brown, on 39, square drove Howell to Cockbain at backward point.
When Smith had Chris Jordan caught behind for 14, Sussex were left needing 84 off the last ten overs with only four wickets in hand.
Smith then took a fine caught and bowled at full tilt after Jofra Archer had skied the ball back over his head and had Ajmal Shahzad well held at deep mid-wicket by Dent.
Beer was run out and when last man Briggs was bowled by Howell, it left Finch, who faced 115 balls and hit 8 fours and a six, high and dry after a fine personal effort.
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