Australia beat US in deciding doubles rubber to reach Davis Cup semi-finals
Olympic champion Ebden and Thompson beat Tommy Paul and Ben Shelton 6-4, 6-4 to put Lleyton Hewitt's side into their third successive semi-final of the men's team event.
The US were slight favourites going into a battle between the two most successful nations in the competition's history, but Australia's Thanasi Kokkinakis beat Shelton 6-1, 4-6, 7-6(14) in the opening singles after saving four match points.
World number four Taylor Fritz then levelled it up with a 6-3, 6-4 defeat of Alex de Minaur to send the tie to the doubles.
Ebden and Thompson's greater doubles experience then proved decisive as they completed the victory.
Australia will find out their opponents later on Thursday when reigning champions Italy take on Argentina.
Hewitt's Australia have been knocking on the door for a few seasons now, losing in the final to Canada in 2022 and falling at the final hurdle again to Italy last year.
"We have such a rich history in this competition and these boys know it's a great honour to wear the green and gold out there," former world number one Hewitt said.
"We've had a very similar team of around six guys who have put their hand up for three or four years now, they have gelled together well, super proud of the whole team."
Hewitt said he had been confident that world number 77 Kokkinakis, who often saves his best for Davis Cup ties, would rise to the occasion against 21st-ranked Shelton.
And so it proved as he prevailed in a thriller. He outplayed Shelton in the first set, but the powerful young American responded impressively to win the second.
As serve began to dominate, the match inevitably went to a tiebreak which was the longest in the Davis Cup for five years.
Kokkinakis led 6-4 but Shelton saved two match points with booming serves and as the tension mounted both players saved match points against them by serving aces.
Shelton banged down two to lead 14-13 but Kokkinakis was not done and reeled off three successive points to claim the win.
"Seeing the boys on the sidelines, seeing Lleyton, obviously an idol growing up, getting super fired up and in my ear keeping me going motivated, I think it's massive," Kokkinakis said.
Fritz repeated his win over De Minaur at the ATP Finals but Australia took full advantage of the Americans' doubles switch.