This time, however, the matchup comes in the semifinals and not in the gold medal game, as it has in the last three Olympics.
The United States won all three of those finals and is seeking its fifth straight Olympic gold medal. The Americans confirmed their role of heavy favourite by defeating Canada 91-48 on Tuesday.
Liz Cambage led Australia with 17 points in a 75-60 win over China.
France will play Russia in the other semifinal.
France advanced with a comeback 71-68 win over the Czech Republic and Russia beat Turkey 66-63 in an equally close game.
Jackson, who finished with 12 points, hit a jumper with 3:46 remaining in the game that gave her 536 points in four Olympics, one more point than former Brazil star Janeth Arcain.
"I am happy, obviously, it's something that's nice, but I hope we win Thursday," Jackson said of the upcoming semifinal against the Americans.
The 31-year-old Australian star was on the losing side in the last three Olympic finals. Australia has to play the U.S. earlier now because it failed to win its group, losing to France.
Cambage and Jenna O'Hea put together an 8-0 run that gave Australia a 55-50 lead late in the third quarter and the Australians never trailed again.
Cambage scored four points in that stretch and had a big block that allowed O'Hea one of her two fast-break baskets.
Jackson's record-breaking jumper put Australia 13 points up and that was the biggest lead until Jennifer Screen hit the last basket of the game. Ma Zengyu led China with 15 points.
The United States turned up the defensive pressure from the start and crushed Canada behind 15 points from Diana Taurasi and 12 from Candace Parker.
The four-time defending gold medallist Americans haven't lost to Canada since playing in the world championship in 1975.
The victory was their 39th straight in Olympic play and came 20 years to the day after the win that started the streak — an 88-74 victory over Cuba for the bronze medal in the 1992 Barcelona Games.
Kim Smith scored 13 points to lead Canada.
Becky Hammon came through late for Russia once again.
The American-born guard scored 19 points, including the go-ahead basket with 13 seconds left.
"It was win or go home and we made some plays down the stretch," Hammon said. "That's the most important thing, we hung in there and stuck it out."
Hammon, 35, is playing in her second Olympics for Russia. She became a Russian naturalized citizen before the Beijing Games and helped her adopted nation win the bronze.
Russia hasn't won a gold medal since 1992 when the country was known as the Unified Team.
The loss ended Turkey's impressive run in its first Olympics.
With the game tied at 62, Hammon got the ball and drove down the lane, scoring with 13 seconds left and drawing the foul.
She missed the free throw and Quanitra Hollingsworth got the rebound. The U.S. born Hollingsworth, who became a naturalized Turkish citizen in May, was fouled and made one of two free throws to make it a 1-point game.
The Russians couldn't put the game away, hitting only two of its four free throws in the final 12 seconds giving Turkey one last chance, but Birsel Vardarli's 3-pointer bounced off the rim.
Celine Dumerc scored 23 points and Enden Miyem made key plays down the stretch as France went 6-0 in the tournament and won another close game to reach its first Olympic semifinal.
France needed overtime wins over Australia and Britain and topped Canada by just four points in pool play.
Dumerc hit the go-ahead 3-pointer with 65 seconds left to make it 67-65, Miyem grabbed an offensive rebound and scored inside the paint to make it 69-65 with 29 seconds left, then sank two free throws to seal the win.
Eva Viteckova scored 13 of her 17 points in the third quarter, when the Czech Republic led by 13.