Matthew Lobb and Clotworthy then chimed in with three wickets each in short order, and Fletcher Coutts claimed one also, so Rangitoto were always under pressure.
At the 34-over mark, they needed 22 more runs with only two wickets in hand. Returning for their second spells, Trimble and Lobb soon took another wicket each to give Boys' High the win by 15 runs.
Next up for Boys' High is a match against Westlake Boys' High, who easily beat Kelston in Monday's other game.
WBHS 103 (Sam Clotworthy 28, Milton Brookland 18, Sam Smith-Bell 12) beat Rangitoto College 88 (Matthew Lobb 4/21, Sam Clotworthy 3/19, Max Trimble 2/16).
Meanwhile, Northland were defeated by Bay of Plenty Coastlands on day one of the Northern Districts primary boys tournament at Hamilton.
BoP Coastlands made 185 while Northland made a gallant effort in their chase to get through to 176 runs, it was not enough for the victory.
BOP Coastlands 185 (J Earle 66, R Clinton 41) beat Northland 176 (C Nitsche 37, J Dey 3/36).