MoM Nash’s first T20 century – 112 not out from 64 balls – helped his side to 222 for 4 then Gayle found left-armer Tymal Mills’ explosive pace too hot to handle and was yorked for five by a delivery timed at 93mph.
Roelof van der Merwe made a defiant 59 and Mahela Jayawardene 51 but Somerset were never in contention and bowled out in the last over for 174 to lose by 48 runs.
Nash and captain Luke Wright laid the platform for Sussex’s second 200-plus total of their Blast campaign with a stand of 156 in 14 overs for the first wicket with Nash making the most of two fielding lapses.
He was dropped on nought off the second ball of the match by James Hildreth at backward point and again in the fifth over by Jayawardene, having scored 17.
Wright did not hit the first six of the innings until in the seventh over but it signalled an onslaught by the Sussex batsmen who plundered 90 off the next eight overs.
Nash was first to his half-century but he was soon overtaken by his partner, who eventually found his timing in his first game of the season after recovering from back and wrist injuries.
Wright’s 83 came from just 39 balls and included five sixes and eight fours as he harnessed a strong wind and targeted the Sea End boundary. It was a surprise when he played on to the leg-spinner Max Waller and Sussex lost Ross Taylor (1) in the next over, caught at long on off a mis-timed drive.
But Nash pressed on and Matt Machan (12) gave him excellent support in a third-wicket stand of 51 from 28 balls. He reached his hundred in the 19th over by hitting Overton over long on for six before gliding the next ball to the backward point rope. He finished with 13 boundaries and three sixes from 64 balls faced. Overton took 2 for 45 but the Somerset attack were guilty of bowling too short.
An asking rate of more than 11 runs an over was always going to test Somerset and they suffered an immediate blow when Ajmal Shahzad bowled Jim Allenby for a duck with the first legitimate delivery of the innings.
But the big moment came in the next over when Mills, with the strong wind at his back, began to bowl consistently at more than 90mph. Gayle guided one ball over the slips for four but when he stepped away trying to hit the next delivery through the off side he was bowled, much to the delight of a 5,500 crowd.
Sussex’s other seamers complemented Mills’ raw pace. South African David Wiese picked up 4 for 38 on his debut and Shahzad ended Somerset’s feint hopes when he had Jayawardene caught at long on for 51 from 39 balls in the 11th over.
Nash said: “We got off to such a good start. Luke Wright helped by taking some of the pressure off with the way be batted on what was a very good wicket to bat on.
“I have been in good nick this season and it was great to take it into this format, I felt pretty calm out there. My first T20 hundred is a special moment and then I thought we bowled and fielded really well. It’s a really good win and we’ve made a good start with two wins out of two and hopefully we can carry it on against Surrey on Friday.”
Sussex captain Wright said: “To beat such a good side like Somerset at this stage of the competition breeds confidence. I thought it was a pretty complete performance.
“Chris Nash batted really well. He gave himself time at the start because they bowled well up top and it paid dividends. I felt a bit rusty but the partnership we put together was crucial.
“I thought we bowled well, especially the seamers who had to bowl into that wind. Tymal Mills has been preparing for a long time for this and getting Chris Gayle out was a massive part of our win.”
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