Jermaine Jones broke the deadlock with his first goal for his country four minutes into the second half after his shot took a deflection off Jamaican defender Jermaine Taylor, giving goalkeeper Donovan Ricketts no chance of making the save.
"I thought we played a good game today," U.S. coach Bob Bradley said. "It took a while to get the goal and the second goal, but certainly as far as establishing our game today I thought we did an excellent job."
Jamaica, which did not concede a goal in the pool stages, were reduced to 10-men when Taylor was red-carded for tripping Jones as he was bearing down on goal.
American striker Clint Dempsey, who rejoined the team on Sunday after missing three days to attend his sister's wedding in Texas, put the result beyond doubt in the 80th minute, side-stepping an advancing Ricketts and tapping the ball into an open net after a low cross from Juan Agudelo.
Landon Donovan, who also missed three days of training to attend his sister's wedding in California, started the game on the bench.
"There are times that players come to you with personal requests," Bradley said. "Ultimately, after speaking at different points with Clint and Landon, I knew how important both of these days were for them. You always try to do what's best for the team and you make tough decisions."
The U.S. have reached the semi-finals in each of the last six editions of the tournament for North and Central America and Caribbean teams and play Panama on Wednesday in a repeat of the 2005 final, which the Americans won on penalties.
Panama, who beat the U.S. in the group stage, sealed their place the hard way, scoring in the 90th minute of regular time to tie El Salvador 1-1 before winning 5-3 on penalties.
Mexico and Honduras will play in the tournament's other semi-final.
The winner of the tournament will represent North and Central America and the Caribbean at the 2013 Confederations Cup in Brazil.
"As the tournament goes on, you start to build team unity. It doesn't happen right away," said Donovan. "We're starting to play as a team. Tonight was a really good performance."
