The final got off to a slow start, with a lack of waves for the first ten minutes. Williams, along with Klein and Naraisa, got mid-range six-point rides but it was Stoyle that broke away with a near perfect 9.5 point ride to take the lead.
Several big sets of waves rolled through the line-up late in the final but Williams, needing a 6.43 point ride to surpass her opponents and take gold, could not capitalise, leaving Stoyle victorious.
Williams will remain in Central America for the next three weeks and will then join up with the New Zealand Surfing team to contest the World Junior Championships in Nicaragua.
Williams' result helped the Kiwi team jump up to 12th after an average start to the event saw them fall as low as 14th on the team standings.
Paige Hareb was the last New Zealand surfer to gain a podium finish at the World Surfing Games, finishing runner up in 2010.