Redmayne danced across the goal line before jumping to the right to stop a shot from Alex Valera and give Australia a well-deserved victory at Ahmad bin Ali Stadium.
Redmayne had joined three minutes from the end of the game for the penalty shootout and became an instant hero with his crosses on the line as he sought to distract the rival kicker.
He danced back and forth, moving his hips and throwing his arms in memory of the clowns of Liverpool’s Bruce Grobbelaar when his team won the 1984 European Cup.
Luis Advincila is enough to shoot his effort against the post and then Valera to save the effort, as Australia qualified for a fifth consecutive World Cup and a sixth in total.
Australia will play Group D in the World Cup with champions France, Denmark and Tunisia. The finals will run from November 21 to December 18.
Australia had missed the first penalty but converted the next five to silence thousands of Peru fans, who traveled for the match and offered noisy support but saw their team evoke few chances.
In contrast, an Australian worker dominated the first exchanges, with winger Martin Boyle cutting the Peruvian defense twice to offer burlesque crosses.
The second half followed a pattern similar to the first with a limited effort on goal until the 80th minute, when Australia suddenly had three good chances to win the game.
Ajdin Hrustic was caught napping as Pedro Gallese lifted a ball over him following a free kick, but the ball hit the bar, rebounding into the keeper’s arms. your shot on the net.
Then, a run down the left wing, Awer Mabil saw his volley fly wide of the mark 83 minutes into the game.
Nine minutes into the match, Australian Mathew Ryan was given a chance to change things around.
Flores then headed against the post when the South Americans found additional equipment in the final stages, but were still unable to resolve the result after two hours of play, setting the stage for Redmayne to emerge as a hero.
The one-match playoffs among the top five finishers in the Asian and South American rankings determined the 31st place in this year’s World Cup.
On Tuesday, the final place in the final will be decided when Costa Rica and New Zealand face off in their intercontinental playoff, also at Ahmad bin Ali Stadium.