Josh Butler returned his best bowling figures in a Guernsey shirt with 3-16 off his four overs as Slovenia were bowled out for just 99 off 19.4 overs.
He took three of the first four wickets – including opener Taher Mohammad for 20 – as Slovenia were reduced to 40-4 off 9.2 overs.
Jack Kovacic offered some big-hitting lower-order resistance as he smashed three sixes in a 16-ball knock of 25.
But he was caught off teenage pace bowler Ed Robinson, who continued to impress with 2-9 off his only over.
In reply Guernsey made heavy weather of their relatively low target – they were 21-2 off three overs as Butler and Tom Nightingale went cheaply.
Lucas Barker (22) and Matt Stokes (16) put on 32 for the third wicket but were dismissed in successive balls to leave the islanders on 53-4 early in the eighth over.
It almost got worse for Guernsey when skipper Ollie Nightingale was dropped on four with the score at 60-4, but a few balls later they lost another wicket as Zak Damarell was caught and bowled by Dileep Pallekonda for four to leave Guernsey on 62-5 off 8.1 overs.
But Nightingale went on to make 18 and Martin Dale Bradley 23 not out as Guernsey reached 103-6 off 14.1 overs.