Somerset had to settle for a point, which put them top of Yorkshire Bank 40 Group C, after rain disrupted their response to the winless Unicorns' 231 for eight at Truro.
Chasing a revised target of 206 runs from 32 overs, following rain in the interval, Somerset smashed 22 off the first two overs - Peter Trego hitting 19 from five balls - before the weather forced the game to be abandoned.
Tom Lancefield had been the mainstay of the Unicorns' innings with 80 from 88 deliveries. Fellow opener Matt Lineker contributed 36 and Scott Elstone 38, with Craig Meschede the pick of the bowlers with 4-43.
Lancefield and Lineker put on 76 for the first wicket, the partnership ending when the latter was bowled by Trego.
Michael O'Shea and Garry Park then departed in the space of three Meschede deliveries in a productive 22nd over.
Lancefield fell to South African slow left-armer Dean Elgar eight overs later, leaving the lower order to keep the Unicorns' score ticking over.
Trego ensured Somerset's reply got off to a blistering start, plundering three fours and a six off Luke Beaven. Skipper Marcus Trescothick was unbeaten alongside him when play was called off.