Somerset made light work of a target of 184 to beat the Unicorns by eight wickets in their Yorkshire Bank 40 Group C opener.
Opening pair Marcus Trescothick and Peter Trego put on 159 in 13.3 overs to ensure an early finish at Taunton.
Trescothick hit seven fours and eight sixes in his 49-ball 87, while Trego was unbeaten on 75 from 38 deliveries - including 10 fours and four sixes - when Somerset got over the winning line from the third ball of the 16th over.
Cumbrian seamer Paul Hindmarch (2-47) took both Somerset wickets to fall with successive deliveries; Trescothick was held at long-off and Jos Buttler holed out to deep backward square-leg for a golden duck.
The Unicorns - a team made up of part-time cricketers looking to get back into the first-class game - had earlier been restricted to 183-8 after being invited to bat.
Ex-Nottinghamshire all-rounder Scott Elstone top scored with 75 not out but received little support from the rest of the line-up.
Seamers Trego (2-33) and Craig Meschede (2-15) both picked up two wickets.