The victory in the third-place game of the CONCACAF championship earned Mexico's second straight trip to the World Cup, and sends them to Azerbaijan September 22-October 13 along with the United States and Canada.
Duarte scored twice in three minutes to give Mexico a commanding 3-0 lead, and then added two more in the 72nd and 84th. Jessica Morales and Hallie Hernandez also scored goals to keep intact Mexico's streak of never having lost to a team other than Canada or the United States in eight matches at the CONCACAF U-17 Women's Championship
Mexico had almost all the possession and chances with Panama only occasionally generating a scoring opportunity.
Goalkeeper Karen Chavarria made several acrobatic saves in the first half to keep Panama within striking distance, coming off her line to thwart Taylor Alvardo twice and diving to her left to block a shot by Karla Nieto at the right post.
But Chavarria, playing her fifth game in 11 days, appeared to be injured on Duarte's second goal in the 54th and was replaced five minutes later by Joselyn Quintero.
After controlling the play early, Mexico went ahead in the 13th minute when an unmarked Morales headed in Nieto's corner kick from inside the six-yard box.
It took until the second half for Mexico to assure its World Cup qualification.
Duarte converted after a Panamanian gaffe. Chavarria came out to punch away Michelle Gonzalez ball into the box, but collided with her own defender, Jaqueline Rodridiguez and was knocked to the ground.
While the ball only went as far as teammate Marta Cox near the top of the area, Chavarria struggled to get back to her feet. Cynthia Pineda knocked the ball away from Cox and it rolled to Hernandez, who crossed it into an unmarked Duarte.
With Chavarria getting to her feet late, Duarte easily headed into an open net. Chavarria then collapsed into the goal with her hand on her lower back.
Duarte scored her second taking a ball on the outer left corner of the area, turning inside Astrid Gonzalez and curling a right-footed ball into the opposite upper corner.
Hernandez, who replaced Morales in the 37th minute, scored one of her own when Duarte intercepted an ill-advised pass by Rodriguez across the top of the Panamanian penalty area and took a shot that was blocked by Yomira Sanford.
The ball rolled back across the area to Hernandez, who took one touch before beating Quintero high inside the near post.
Duarte added two more to give her five for the tournament and Mexico its 14th goal in five games.