In the 36th minute Canadian defender Paul Staltieri was called for an infraction as Martinez attempted a bicycle kick. Martinez drilled his ensuing effort from the spot past diving Canadian goalkeeper Greg Sutton.
Canada nearly equalized in the 56th, when Patrice Bernier crossed to an open Josh Simpson. Honduran keeper Donis Escobar did well to make a diving save and preserve the lead.
The victory was celebrated by thousands of Honduras fans in the crowd, who waved the country's flag and draped it over railings in several sections of the stadium. It was a welcome cause for celebration for a country in turmoil. Honduras coach Reinaldo Rueda said his team was "dedicated to offering peace and tranquility."
"It's difficult for all of us," said Martinez, who applauded the fans as he came out of the game in the 72nd minute. "Coach has his family in Honduras as do all of us."
Martinez said he wanted to take the opportunity to ask the government to "seek peace."
The defeat ended Canada's hopes of claiming the title for the first time since 2000. Honduras, who fell to the USA in the 1991 final and in the 2005 semi-finals of CONCACAF's bienniel showpiece, will travel to Chicago to face the winner of the quarter-final between the US and Panama.
In the other two quarter-finals, Guadeloupe face Costa Rica and Mexico take on Haiti today. The final is on 26 July at Giants Stadium in East Rutherford, New Jersey.