New Zealander Nicol scored a brilliant 133 with seven fours and seven sixes as Gloucestershire ran up an imposing 290 for six batting first, with his countryman and opening partner Hamish Marshall contributing 47 while Fuller added a quickfire 40 late on.
Fuller, who conceded 38 off one over as Gloucestershire lost their Friends Life t20 quarter-final to Sussex on Tuesday, then shone with the ball, taking six for 35 off his six overs as Holland were bowled out for 146 in the 22nd over.
A rain interruption had seen Holland's victory target changed to 237 off 28 overs, but they never seriously threatened and ended up losing by 90 runs.
Tom Cooper top-scored for the Dutch with 51 but he was part of a major Holland collapse which saw the home side lose their last eight wickets for 43 runs in under eight overs.
Gloucestershire's victory sees them join second-placed Holland on 11 points in Group A, one point behind leaders Middlesex but with the west country side having played a game less than both their rivals.
Lancashire are fourth in the group on 10 points but with two games still in hand on Gloucestershire, who they meet at Old Trafford on Monday.