S. won their first group stage game against Honduras and have six points from two games, while Panama have two points, Honduras and Haiti one point each.
The U.S. meet Panama in their final group match, while Honduras plays Haiti. The top-two qualify for the quarter-finals with the two best-placed third teams also advancing.
Though the U.S. and Haiti were deadlocked at half-time, the Americans were unlucky to have an Aron Johannsson goal disallowed for offside.
U.S. coach Jurgen Klinsmann sent on Gyasi Zardes at half-time in place of fellow striker Jozy Altidore, a move that paid quick dividends when the Los Angeles Galaxy player found Dempsey with a perfect pass that led to the game’s only goal.
“He made a great play for us and we’ll count on him to continue making some big plays for us,” American captain Michael Bradley said of Zardes.
Earlier, Panama and Honduras played an ill-tempered match during which tempers boiled over several times in the second half as referee Marlon Mejia struggled to keep control.
Panama’s players were particularly incensed, especially when they were denied two penalties and had defender Luis Henriquez sent off for a second yellow, while four others were booked.
Two Honduras players were also booked.
A draw was probably a fair result, though Honduras had two chances in added time when Romell Quioto missed from five yards out before Eddy Hernandez had a goal ruled out for offside.
It was the second goal by Hernandez disallowed for offside.
Panama took the lead in the 21st minute when Luis Tejada scored from a well-worked set piece and they had two strong penalty appeals, one either side of half-time, though the referee remained unmoved.
Honduras had the better of the final 30 minutes and were rewarded in the 78th minute when Andy Najar was tripped inside the box and Mejia pointed at the spot, sparking a full-scale melee between the players.
It took officials a full three minutes to restore order.
Andy Najar’s penalty attempt was then brilliantly pushed on to the crossbar by Panama keeper Jaime Penedo but the ball cannoned back to the feet of Najar, who made the easy tap-in before celebrating with an acrobatic backflip.
Three minutes later, Panama’s players again remonstrated with Mejia and Alberto Quintero was lucky to avoid a red card when he made clear contact with the official.
Even the final whistle did not signal the end of their complaints as Panama players continued to remonstrate with the referee at the edge of the pitch.
(Reporting by Andrew Both in Cary, North Carolina; Editing by Greg Stutchbury)