The pair, key players for the Wallabies, missed last weekend's heart-stopping quarter-final against Scotland because of injuries but were cleared to return the starting lineup making it through training on Friday.
Their availability is a major boost to an Australian side that struggled to produce their best against the Scots, needing a last-minute penalty to secure a 35-34 win.
Pocock, in particular, is considered crucial to Australia's chances of beating the Pumas because of the way the powerfully built number eight dominates the breakdown and creates turnovers.
Folau is also a pivotal part of Australia's game plan because of his ability to catch high balls and break tackles when he has possession.
Loose forward Ben McCalman and utility back Kurtley Beale reverted back to the bench.
There was one casualty from the Scotland game, however, with loosehead prop Scott Sio failing to recover from an elbow injury.
Sio, instrumental in helping restore confidence to Australia's wonky scrum, was replaced in the starting lineup by James Slipper, who earns his 73rd test cap, a record for an Australian prop.
Slipper almost derailed Australia's World Cup when he threw the intercept pass that allowed Scotland to take the lead from Australia in the dying stages of the quarter-final.
“James has been pushing for a starting spot with his performances as a finisher and I know he’ll take it with both hands," Cheika said in a statement.
"James is a leader in our squad and has performed well through this tournament so far and in the lead-up matches.
With Slipper promoted to the starting lineup, Toby Smith took his spot on the reserves bench.
Drew Mitchell also retained his place on the wing, needing just one more try to draw level with Bryan Habana and Jonah Lomu as the all-time Rugby World Cup leading try scorer.
“This weekend is a great opportunity for the lads to improve on last week and take advantage of the chance to play on such a big stage," Cheika said.
"This weekend we want to make Australia proud of their team.”
Team: 1-James Slipper, 2-Stephen Moore (captain), 3-Sekope Kepu, 4-Kane Douglas, 5-Rob Simmons, 6-Scott Fardy, 7-Michael Hooper, 8-David Pocock; 9-Will Genia, 10-Bernard Foley, 11-Drew Mitchell, 12-Matt Giteau, 13-Tevita Kuridrani, 14-Adam Ashley-Cooper, 15-Israel Folau
Replacements: 16-Tatafu Polota-Nau, 17-Toby Smith, 18-Greg Holmes, 19-Dean Mumm, 20-Ben McCalman, 21-Nick Phipps, 22-Matt Toomua, 23-Kurtley Beale
(Editing by Ed Osmond)
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