However, Joyce fought back and showed her top seed billing with a comfortable 11-6 win in the second set.
The third was a classic with neither player being able to pull away. However, Joyce picked up the crucial break to win it 14-12.
Holst couldn't scrap her way back into the match, eventually going down in four sets.
Meanwhile top seed Trimble and Auckland's Matthew Lucente went through a titanic struggle to decide the Under 19 Boys.
The pairing went back and forth as they each dominated two of the opening four sets to set up a final showdown in the fifth.
Lucente picked up the ascendancy and clinched a comfortable victory in the final set to claim the title.