He had Liam Banks stumped before bowling Harry Brook for a golden duck with a perfectly-pitched wrong-un to leave England 2/47.
Pope added a third scalp, England No 4 Will Jacks for one, in his third over to make it 3/51 and give Australia some hope of a miracle.
Impressive English opener Tom Banton seized back some control of the match with a six off Pope to bring up his fifty as England moved past the halfway mark in its chase at 3/67 from 13 overs.
But Pope kept coming. He answered by taking his fourth wicket and the key scalp in Banton (58) as the English opener hit a reverse sweep straight to Sangha at gully.
The leggie made it five two overs later, removing Fin Trenouth for five to leave England needing 49 runs with five wickets in hand as the players broke for lunch.
England looked to see Pope off when play resumed. A wide delivery was the only run from his sixth and seventh overs and the English nerves were well and truly setting in when offspinner Param Uppal joined the party by dismissing Euan Woods for eight.
Nerves became pure panic as Tom Scriven was run out to leave England 7/82. Pope took his tally to six in the following over to make it 8/84.
England was 8/96 as Pope began his 10th and final over but he only need four deliveries. Ethan Bamber was trapped LBW for two and No 11 Dillon Pennington was bowled for a duck as the Poms were all out.
Pope's figures were the best ever recorded at an under-19 World Cup.
Earlier, captain Jason Sangha (58) was the only batsman to make a mark as Australia was knocked over inside 34 overs.
The rest of the batting lineup was roadkill as English bowlers Ethan Bamber, Dillon Pennington and Will Jacks took three wickets each.
In reply, England raced to 0/47 from seven overs as Banton took a liking to Aussie quicks Ryan Hadley (0/24 from four overs) and Zak Evans (0/17 from two overs). After three subpar knocks in the group stage, Banton hit two sixes off one Evans over as he surged towards a half-century.
Australian under-19 coach Ryan Harris made a bold decision to drop Steve Waugh's son, Austin, for the knockout game.
Austin Waugh had endured a slow start to the tournament in New Zealand, making knocks of six and 26 and taking 1/64 in his only innings with the ball as the Aussies' failed to impress during the group stage.
They were comfortably beaten by India in their opening game before thumping minnows Zimbabwe and Papua New Guinea. England went undefeated against Bangladesh, Canada and Namibia.
But Waugh couldn't even consider himself the most unlucky to miss selection against the Poms. Fast bowler Jason Ralston was overlooked despite taking 7/15 against PNG. Jarrod Freeman, who made 11 and took 0/11 from nine overs in Australia's final pool game, was the other player to make way.
