The unbeaten Americans had already clinched their spot in the quarter-finals from Group A before the match.
In a physical, testy, battle at Sporting Park in Kansas City, they had to overcome a 1-0 half-time deficit with a 54th-minute close range goal from former Aston Villa midfielder Michael Bradley.
Haiti, meanwhile, advanced to the knockout phase by beating Honduras 1-0 courtesy of a Duckens Nazon goal.
Panama, who drew all three of their games at the tournament to finish on three points, will now have to wait to see if they can qualify as one of the two best third-placed teams from the groups.
The Central Americans came out inspired on Monday, looking for their first win and Luis Tejada appeared to have given them the lead in the 10th minute only for the goal to be ruled out for offside.
Panama did finally score in the 34th minute when Blas Perez finished off a pass from Tejada.
The United States struck back early in the second half as Alejandro Bedoya played a great ball into the box for Bradley to finish.
The match had several testy moments with three Panamanians receiving yellow cards.
Bradley said: “It’s always tricky when you have one team who has advanced and another team playing for everything. At the end of the day we’ll take our points and move on.”