Winless in eight matches dating back to July last year, Panama finally ended that run with the victory at the Estadio Rommel Fernandez Gutierrez.
Hernan Dario Gomez's men had to wait until midway through the second half to take the lead.
Darwin Pinzon made it 1-0 in the 67th minute before Juan De Gracia doubled their advantage moments later.
Pinzon was on the scoresheet once more with 16 minutes remaining, and Ismael Diaz completed the stunning period with a goal in additional time.
Returning to winning ways came at the perfect time for Panama, who are competing at the Copa Centroamericana in the United States in September.