son of coach Bob -- could not deny the U.S., who were left to celebrate a historic victory.
The Americans started brightly and Spain goalkeeper Iker Casillas found his goal under threat from Altidore and Charlie Davies early on.
Davies' then threatened again with a glancing header across the face of goal, and when Dempsey drilled a 25-yard shot just wide in the eighth minute, the Spaniards must have wondered what was going on.
The world's top-ranked side did not take long to fashion some chances of their own, though.
Cesc Fabregas sent a dipping shot over the bar and then the Arsenal captain threaded over a superb cross that Fernando Torres was just unable to convert at the far post.
That was all in a breathless opening 12 minutes, and both sides continued to push forward before the U.S. took a shock lead through Altidore in the 26th minute.
Dempsey played the ball into the striker on the edge of the box and the 19-year-old was allowed to turn Villarreal teammate Joan Capdevila far too easily before firing in a shot that Casillas got his hand on but could not keep out.
That was the first goal Spain had conceded in their Confederations Cup campaign and only the third since Vicente del Bosque took over last summer, with this being the 14th match under the former Real Madrid boss.
The Spaniards were under real pressure and, after David Villa had blazed a half-chance over the bar, the U.S. had a great opportunity to make it 2-0.
Two Americans were unmarked at the far post as they raced in to meet Landon Donovan's free-kick, but while captain Carlos Bocanegra was probably the better placed, Dempsey stretched to get his head to the ball and could not get it on target.
Despite that wasted opportunity, the U.S. still held onto their 1-0 lead until the break, with Tim Howard sticking out a foot to deny Torres at his near post just before the interval.
With their proud record in danger, Spain came out at the start of the second half with all guns blazing.
Just two minutes after the re-start Howard produced a superb save to tip away Villa's effort, before Xabi Alonso fired a rising shot just over the crossbar.
It was all one-way traffic and Villa and Albert Riera both tried their luck, while Xavi had a good shout for a penalty following a challenge by Donovan inside the area.
The shots continued to rain in on Howard's goal, with the Everton custodian doing well to keep out efforts from Fabregas and Sergio Ramos in quick succession.
Spain could not find the breakthrough, though, and their hopes of reaching the final were crushed when Bradley's boys netted their second goal in the 74th minute.
Donovan's low cross should really have been cleared by Ramos at the far post, but Dempsey showed quick reactions to prod the ball away from the Real Madrid defender and past Casillas.
Spain got a brief glimmer of hope when Bradley was shown a red card for a heavy challenge on Alonso, but Del Bosque's side could not take advantage as they slumped to their first loss since going down 1-0 at home to Romania in a friendly in November, 2006.
