Abdiel Arroyo opened the scoring for Panama in the 16th minute when he beat a defender and Guyana's goalkeeper to a long pass and fired it into an empty net.
Guyana equalised through a 33rd minute penalty by Neil Danns but an own goal by defender Terence Vancooten seven minutes later put Panama back in front 2-1.
Erick Davis converted a penalty early in the second half to pad Panama's lead to 3-1. Davis' first attempt was saved but the referee ordered it to be retaken after the goalkeeper moved off his line.
Gabriel Torres' 86th minute goal put Panama ahead 4-1 before another penalty by Danns, this one in stoppage time, capped the scoring.
Panama next face the United States on Wednesday in Kansas City while Guyana take on Trinidad and Tobago.
(Reporting by Rory Carroll' Editing by Peter Rutherford)
