Converted tries from Rocky Elsom and Quade Cooper gave the Wallabies a well-deserved 14-0 lead at half-time.
Tries from Denis Leamy, Tony Buckley and Doug Howlett helped the Irish province to a 21-10 half-time lead.
But two tries from Leroy Cudjoe and one from Luke Robinson turned it round.
But further tries from Mark Calderwood and Sean O'Loughlin helped Wigan into the last four.
Gloucester raced to a healthy lead with tries from Luke Narraway, Alasdair Dickinson and Eliota Fuimaono-Sapolu.
England's strength showed after the break with quick tries from debutant Peter Fox and Keith Senior.
They dominated the first half territorially but only produced two tries from debutant Michael Jennings.
Edinburgh, with tries from wingers Tim Visser and Mark Robertson enjoyed a 14-11 interval advantage.
First-half tries from Lucas Borges and Horacio Agulla did the main damage on the scoreboard.
Second-half tries from Joe Gray and Ugo Monye also helped Harlequins to their second straight win.
Tries from Chris Henry and Fergus McFadden helped the Irish lead 17-0 at the break.
Tries from Will Harries and Matthew Watkins helped the Dragons into a healthy 21-10 first-half lead.
Tries from Brian Liebenberg and Christophe Dominici put Stade into a comfortable 17-3 half-time lead.
The Londoners salvaged some respect with well-worked tries from second rower Haumono and full-back Luisi.
Clermont regrouped and long-range tries from Aurelien Rougerie and Vilimoni Delasau set up a dramatic finale.
But Warrington led at the break with tries from Tawera Nikau and Alan Hunte.
But two early second-half tries from Richie Myler settled England's nerves, before Kevin Sinfield added another.
Two quick tries from Paul Deacon put Wigan firmly in control after the break as they asserted their dominance.
But second-half tries from Rooney, Tony Martin and Sam Obst saw Wakefield complete a stunning comeback.
The Highlanders had led with first-half tries from Aisea Tuilevu, Josh Blackie and Seilala Mapusua.
Blackpool only trailed 24-16 at half-time after tries from Martin Ainscough, John Clough and Damian Munro.
However, injury-time tries from replacement Des Dillon and Gordon D'Arcy brought Leinster's total up to 48.
The Warriors were 10-0 down after only six minutes following tries from Jason Demetriou and Tevita Leo-Latu.
But Cas sealed the match with tries from Michael Wainwright, Kirk Dixon, Michael Shenton and Brent Sherwin.
Two tries from Jon Wilkin further compounded the visitors' misery, while Gareth Ellis scored a consolation try.
Tries from Jamie Heaslip and Keith Gleeson helped the home side into a 18-3 lead by half-time.
Wigan made the last four with further tries from Richards, Josh Charnley (2) and skipper Sean O'Loughlin.
Tries from Anthony Blackwood, Lincoln Withers and Matt Smith made sure of the victory at Brewery Field.
Rovers led through tries from Jake Webster and Louis Sheriff, with Oliver Wilkes and Luke Gale levelling.
Saracens, whose team included nine South Africans, struck back with tries from Ernst Joubert and Brad Barritt.
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