With the teams locked at 1-1 after extra-time, Panama converted all five penalties they attempted and El Salvador missed their first spot-kick from substitute Dennis Alas.
El Salvador opened the scoring in the 78th minute when striker Rodolfo Zelaya, who missed a penalty attempt in the first half, converted a second penalty attempt after he was brought down by defender Roman Torres.
El Salvador looked certain to hang on and advance to the semi-finals for the first time until Panama evened the score after a late goal-mouth scramble.
From close-range, Luis Tejada got a header that was ruled to have crossed the line. Tejada also converted the decisive spot-kick in the shootout.
Panama will now play the U.S. Wednesday's in Houston after the Americans beat Jamaica 2-0 in the earlier quarter-final at RFK Stadium in Washington DC.
The U.S. defeated Panama on penalties in the 2005 final final but Panama beat the host-nation in the group stages last week to raise hopes of another win this week.
The other semi-final will be played between Mexico and Honduras.
The eventual winner of the tournament will represent North and Central America and the Caribbean at the 2013 Confederations Cup in Brazil.
