"Now we have to go out and beat Germany, that's what we have to do," U.S. coach Jurgen Klinsmann said. "We have to play Germany, we have one less day to recover, we played in the Amazon, they played on a place with less travel. We have to do it the tough way."
Dempsey's goal was his fourth at a World Cup and second at this year's tournament. Jones scored his third goal for the United States national team and first in almost two years.
It was all Portugal for much of the first half, with Ronaldo in the starting lineup but getting less involved as the match progressed. The Americans, however, started to get more and more chances and even had a shot from Michael Bradley cleared off the line by Ricardo Costa in the 55th.
"There didn't seem to be any problem with Cristiano Ronaldo," Portugal coach Paulo Bento said. "What happened during the game has something to do with our other players."
The heat in the Amazon rainforest, however, seemed to slow the Portuguese as the match wore on.
In the 39th minute, referee Nestor Pitana of Argentina called for a cooling break, the first such decision to be taken at this World Cup.
At the start of the match, FIFA listed the temperature at 30 degrees C (86 degrees F) with 66 percent humidity. FIFA uses the "Wet Bulb Globe Temperature" to determine when official cooling breaks should be added, and says the WGBT must be above 32 degrees C (90 degrees F) for them to be considered.
The breaks are supposed to occur in the 30th and 75th minutes. There was no break in the second half, but that didn't stop Ronaldo from creating the final goal.
"It was a thriller," Klinsmann said. "Everybody who had a chance to be today in Manaus will talk about this game for a long time."
United States: Tim Howard; Fabian Johnson, Geoff Cameron, Matt Besler, DaMarcus Beasley; Kyle Beckerman, Jermaine Jones, Alejandro Bedoya (DeAndre Yedlin, 72), Michael Bradley, Graham Zusi (Omar Gonzalez, 90); Clint Dempsey (Chris Wondolowski, 87).
Portugal: Beto; Andre Almeida (William Carvalho, 46), Ricardo Costa, Bruno Alves, Joao Pereira; Miguel Veloso, Joao Moutinho, Raul Meireles (Varela, 69th), Nani, Cristiano Ronaldo; Helder Postiga (Eder, 16th).