Ollie Robinson's 53 helped Kent to what looked a below-par 165-9 at Canterbury.
But, having confidently reached 54-1, Somerset collapsed to 124 all out, with Pakistan's world number one Twenty20 batsman Babar Azam falling for seven.
In Saturday's other game, Mark Watt and Billy Godleman starred for Derbyshire as they opened with a five-wicket victory over Yorkshire.
Slow left-armer Watt took 4-19 as the Vikings made 164-8 from their 20 overs - having at one point been 77-6.
Only a late cameo from Jordan Thompson dragged them towards a competitive score, clobbering five sixes as he made 50 off 27 deliveries.
England white-ball specialist David Willey dismissed Flynn Hudson-Prentice early on, but an unbeaten 70 from captain Billy Godleman saw the Falcons over the line with five balls left.
The wicket of Hudson-Prentice aside, it was a night to forget to Willey, who made just six batting at number three and returned figures of 1-29 off 3.1 overs with the ball.
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