The French keeper failed to hold a shot from Craig Dargo and Graham Bayne was first to react and hook the ball into the net.
This result leaves Rangers ten points behind leaders Celtic after only ten games which already looks too big a gap to close.
The home team forced some early corners but it took a 35 yard strike from Phil Bardsley after 20 minutes before the visitors' keeper Mark Brown was called into action.
Despite home pressure it was just before hal- time that Rangers created their first clear cut chance. Filip Sebo slid a clever pass to Thomas Buffel, but Brown raced quickly from his line to narrow the angle and block.
Eighteen minutes from time the roof fell in for the home team as the Highlanders scored. Letizi spilled Dargo's shot and appeared slow to react, with Bayne able to reach the loose ball first before finding the net for a famous winner.
Rangers were then denied the penalty in the closing minutes when Nacho Novo appeared to be pulled down.