The Americans beat European champion Italy 9-6 to reach the last four. Hungary and Spain will meet in the other half of the draw following victories in the quarterfinals.
Hungary overcame a four-goal effort from Evgeniya Ivanova to beat Russia 11-10, while Spain held off a late Britain rally to secure a 9-7 win over the host nation.
In a physical, bruising match that ended with five players fouling out, Australia and China each hit shots with time running low — Australia in regular time, China in extra time — to push the game to penalties.
Goalkeeper Alicia McCormack made one stop and then Gao Ao hit the left post for China's second miss of the shootout, giving Rippon the chance to win the game, and she calmly fired the ball in and put Australia through to the semifinals.
"The girls hung in there, did it tough," Australia coach Greg McFadden said. "They have been practicing penalty shootouts since September and three of the girls who had to take them weren't in our list to take them and they stepped up."
Winless in the preliminary round, China never backed down against an undefeated Australia team and almost pulled off the upset in regular time, but Holly Lincoln-Smith scored from long range with 35 seconds to play in the fourth to level the game 14-14 and force overtime.
"I've thrown it a few times, but I definitely only pull it out when necessary," Lincoln-Smith said of her no-look, spinning equalizer. "I couldn't sleep last night I was thinking about throwing that shot. I've been sick and I was wondering if I had the strength to throw that shot from so far out, but I thought I have nothing to lose right now so I just threw it.
"I felt the moment was right, that the goalkeeper wouldn't be ready."
Australia scored first in extra time, and led 16-15 with less than a minute to play before Sun Huizi rose out of the water to flip in a pass from Sun Yujun and force the shootout.
Melissa Seidemann scored three goals and captain Brenda Villa added two more as the U.S. recovered from a 2-0 deficit to set up a rematch of the semifinals from Beijing four years ago the Americans ultimately won.
"We play similar styles and we've been consistently two of the best teams in the worlds," said U.S. coach Adam Krikorian after beating the Italians for just the second time in 11 meetings at major tournaments. "They're one of the most talented teams. It's gonna be a heck of a game."
Maica Garcia, with her head underwater, squeezed a no-look, behind-the-back shot past Britain goalie Robyn Nicholls with 27 seconds left to re-establish a two-goal lead and secure victory for Spain, which is in position to secure its first Olympic water polo medal.
Earlier, Dora Antal scored on a rebound with just over a minute to play and goalkeeper Flora Bolonyai made a save at the buzzer for Hungary to edge Russia.
Antal pounced on a loose ball in front of goal after a Rita Keszthelyi shot rattled the post and flipped the ball past goalkeeper Anna Karnaukh to give Hungary a two-goal lead.
Olga Beliaeva converted a penalty with 56 seconds left to pull Russia back within a goal before Bolonyai preserved the victory with her block.
"My team is very young so this is a new experience for them," Hungary coach Andras Meresz said. "This is the best Hungarian team in 20 years, so I am very happy to take them to the semifinal."
Ryan Lucas can be reached on twitter at www.twitter.com/relucasz