The Americans will meet either Mexico or Honduras in Saturday's championship match.
Tim Howard produced the U.S. shutout and kept the game scoreless in the 71st minute by stopping a hard shot from Armando Cooper inside the penalty area.
Landon Donovan and Freddy Adu, both of whom came off the bench, combined to set up Dempsey for his goal 5 minutes later.
Adu sent a pass to Donovan from midfield and the American striker carried the ball down the right side before cutting into the area. He got off a low crossing pass across the face of the goal for Dempsey, who stabbed at the ball with his left foot and nudged it into the net from close range.
The United States gained revenge for a 2-1 loss to Panama in the group stage of this tournament, which brings together national teams from the CONCACAF region of the soccer's world governing organization.
The winner of this event will qualify for next year's Confederations Cup.