The United States kept their basketball gold medal dreams alive Tuesday by grinding past world champions Spain and into the semifinals, while Slovenia crushed Germany to make the last four on their Olympic debut.

Sharp-shooting Brooklyn Nets star Kevin Durant poured in 29 points and four assists while Boston’s Jayson Tatum chipped in 13 in a battle between the world’s top two teams, nullifying Ricky Rubio’s 38-point spree for Spain.

The three-time defending Olympic champions will now face either a Patty Mills-led Australia or a dangerous Argentina to decide who plays the final on Saturday.

Slovenia progressed on the back of 27 points from Zoran Dragic and another 20 from Dallas Mavericks star Luka Doncic in their 94-70 rout of Germany and will next meet either France or Italy.

Gregg Popovich’s U.S. team came to Tokyo with two shock defeats in exhibition games and then crashed in their opener against eventual Group A winners France — their first defeat at an Olympics since 2004.

But they have steadied the ship and came through a see-sawing clash with Spain after knuckling down in the final stretch to go 13-0 against their rivals in Olympic competition.

Minnesota Timberwolves guard Rubio drilled 13 points to put Spain into a 21-19 lead after the first quarter as the U.S. gave up a seven-point advantage.

They traded the lead in a back-and-forth second quarter before Spain went on an 10-point run to move 39-29 clear.

But inspired by Durant, the U.S. fought back and a basket from inside the paint from Devin Booker with seconds to go drew them level 43-43 at the break.

The tide looked to turn in the third quarter with the U.S. going on a 22-6 run to take charge before Spain regained ground to go into the final quarter just six points adrift at 69-63.

With their reputation at stake — they have won medals in all 18 Olympics they have competed at, winning 15 gold, a silver and two bronze — the U.S. put their heads down to ensure they stayed in the tournament.

Earlier, world No. 16 Slovenia continued their dream run against a German side ranked a place below them and who only scraped into the quarters on point differential.

“We knew it was not going to be an easy game. Even though everybody before the game expected us to win easy, it wasn’t easy,” said Slovenia coach Aleksander Sekulic.

“These guys, they put their hearts out on the court. They just bleed on the court for the team.”

Small forward Dragic, who plies his trade in Spain, was at the heart of the action with six rebounds and four assists to go with his 85% scoring percentage.

Maodo Lo put on 11 for Germany, who were back in the Olympics for the first time since 2008, when they were led by all-time great Dirk Nowitzki.

Slovenia dropped 25 points in the opening quarter to gain an 11-point cushion before Germany staged a comeback in the second period, inching 32-31 in front.

But that was the only lead they had as Slovenia rallied with Dragic bagging his fifth straight field goal with a 3-pointer to send them into halftime with a 44-37 advantage.

He nailed another 3-pointer seconds into the third quarter to pull them 12 points clear. They kept up the offensive pressure and never looked back.

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