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 (four for 43) the pick of the bowlers.
Lancefield and Lineker put on 76 for the first wicket, the partnership ending when the latter was bowled by Trego.
Michael O'Shea (19) and Garry Park (nought) 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 Elstone, Devon Endersby (one), Lewis Hill (five), captain Keith Parsons (16) and Luke Beaven (six not out) to keep Unicorns' score ticking over.
Trego ensured Somerset's reply got off to a blistering start, plundering three fours and a six off Beaven during his five-ball 19 not out. Skipper Marcus Trescothick was unbeaten on three when play was called off.