The United States will now face fierce regional rivals Mexico in Sunday's final at Soldier Field in Chicago.
New Chelsea signing Pulisic bundled home a rebound from Jordan Morris's shot in the 52nd minute to give the US a 2-0 lead after a storm in Nashville had forced the players off for almost an hour and a half.
The defending champions had taken the lead through a superb Weston McKennie ninth-minute strike following a dominant opening spell which saw them carve out a series of chances.
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Schalke 04 player McKennie was a constant threat for the hosts, who had already gone close to scoring through Paul Arriola and Reggie Cannon when veteran midfielder Michael Bradley sprayed a pinpoint pass to Cannon on the flank.
FC Dallas fullback Cannon crossed into the area, and after the ball rolled past Jozy Altidore, McKennie swept home.
Pulisic almost doubled the lead in the 12th minute when his free-kick from the left tested Jamaica goalkeeper Andre Blake, who parried away.
The bright US opening was halted four minutes later when an electrical storm rolled into the region.
With lightning a possibility, tournament officials called the players off the field and cleared the stands.
It was another hour and 27 minutes before play could resume, and the US were slow to regain their rhythm.
But they started the second half brightly and when Morris unleashed a well-struck shot Blake was unable to hold on. The rebound fell into the path of Pulisic who jabbed home an opportunistic strike.
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Substitute Gyasi Zardes squandered a golden chance to make it 3-0 moments later after being released by a superb first time McKennie pass, lashing his shot well wide.
Jamaica gave themselves a lifeline in the 69th minute when substitute Shamar Nicholson nodded home a cross after Leon Bailey's driving run to make it 2-1.
But with time running out for the Reggae Boyz, Arriola's shot from distance was half-saved by Blake and Pulisic was once again on hand to bury the rebound.
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