Chasing 287 for victory in Ahmedabad, England folded for 253 in 48.1 overs despite a valiant 64 from Ben Stokes to slump to their sixth defeat in seven matches and stay bottom of the 10-team table.
Five-time champions Australia edged closer to securing a semi-final berth alongside India and South Africa - both already qualified for the last four - with their fifth straight win.
Zampa returned figures of 3-21 with his leg-spin to puncture England’s hopes that were raised by a couple of partnerships including a 63-run fifth-wicket stand between Stokes and Moeen Ali, who hit 42.
“We put on a really competitive total, but it was going to be tough to defend,” said Zampa.
“The ground felt really dewey, really wet. So length control, attacking the stumps, trying to guess what the batsman was going to do was really important.”
Zampa, who had earlier hit 29 with the bat, dismissed Stokes when the English star mistimed a paddle to be caught at short fine-leg and departed with a shake of his head.
Wickets kept tumbling with Liam Livingstone and Moeen falling in quick succession for a familiar England tale in this tournament where they have also lost to Afghanistan and Sri Lanka.
Zampa, who leads the World Cup bowling chart with 19 wickets, also took a superb outfield catch to help dismiss David Willey.
“It certainly feels like a low point. I’ve had a few but definitely as a captain,” said England skipper Jos Buttler.
“To be stood in this position having arrived in India with high hopes is incredibly tough and disappointing. It hurts a lot,” he added.
Left-arm Mitchell Starc struck with two early wickets for Australia including Jonny Bairstow on the first ball of the chase and then Joe Root for 13.
Dawid Malan made 50 before skipper Pat Cummins took him out.
England, in their remaining two matches, are left to fight for a place in the 2025 Champions Trophy with the top seven teams from this World Cup gaining entry into the tournament where hosts Pakistan will have automatic qualification.
Batsmen set up victory for Australia with Marnus Labuschagne top-scoring with 71 and useful contributions from Steve Smith (44), Cameron Green (47), Marcus Stoinis (35) and Zampa (29 off 19 balls).
Chris Woakes returned figures of 4-54 and was supported by fellow quick Mark Wood and leg-spinner Adil Rashid, with two each, to help bowl out Australia for 286.
Woakes struck early to remove the openers including previous-match centurion Travis Head, for 11, and David Warner, for 15.
Steve Smith and Labuschagne put on 75 runs to steady the innings but Rashid broke through.
Rashid dismissed Smith and then had Josh Inglis (three) caught at backward point after the batsman attempted a reverse sweep.
Labuschagne reached his 50 and put on a partnership of 61 with Green before falling to Wood. He made 71.
Green and Stoinis, the two players coming into the team in place of Glenn Maxwell and Mitchell Marsh, put on 45 for the sixth wicket.
Rain helps Pakistan keeps hopes alive
Earlier yesterday, Fakhar Zaman and captain Babar Azam starred as Pakistan pulled off a dramatic, rain-hit 21-run victory over New Zealand to keep their hopes of progressing in the tournament alive.
After New Zealand had piled up a mammoth 401-6, Pakistan were 160-1 in the 21st over when rain brought a stoppage.
Set a revised target of 342 off 41 overs, Zaman had moved to 126 and Azam was on 66 with their team on 200-1 in the 26th over when the rain returned, this time bringing the game to an end and Pakistan declared the winners as they were ahead of the required rate.
Pakistan and New Zealand both have eight points and remain in contention for semi-final spots with a match each left to play in the group stage.