The result completed an 8-1 aggregate victory after Cox scored the eventual winner in the 71st minute to give Panama a 2-0 lead. Karla Riley put Panama ahead 1-0 in 21st minute before Sheyla Flores scored in the 81st for Panama.
Cox scored two goals three minutes apart (in the 59th and 62nd minutes) in Wednesday's 6-0 first leg victory over Nicaragua while Riley had a goal in the 58th.
Panama, seeking a second straight trip to the U-17 finals, will face Costa Rica on December 7 and December 11 to claim Central America's second berth along with host Guatemala in the May 2-13 tournament. The first leg is set for Panama with the second in Costa Rica.
Besides Guatemala, Canada, Mexico and the United States qualify automatically for the eight-team field along with three Caribbean sides, which will determine its teams in its final round of qualifying Tuesday-Saturday in Kingston, Jamaica.