Everton's captain, Jagielka, has not been ruled out but Gareth Barry is expected to miss the semi-final with a groin injury that forced his withdrawal at half-time against Liverpool.
However, the Saffrons then suffered a massive blow as Niblock - who had been dominating his battle with McAdam - suffered an ankle injury which forced his departure at half-time.
Given this would have cut the capacity in half and forced his team-mates to change in the corridor, his request was politely declined.
Four minutes later the Wigan hooker Sam Powell forced his way over from dummy half and, before Wakefield had time to regroup, the centre Oliver Gildart followed up Williams's grubber kick to send the left-winger, Josh Charnley, over.
Makeshift hooker Bailey forced his way over from dummy half to open the scoring after front-rower Antonio Kaufusi was stopped short of the line.
O'Loughlin gave his side renewed hope when he forced his way over from acting half-back five minutes from the end, but Wane's men were beaten.
There was a very competitive two-minute period when Hamilton, Massa and Rosberg took it in turns to go top but it was Hamilton who remained there, forcing his McLaren to go half a second faster than anyone else.
Huddersfield went back in front on the hour when McGillvary cut inside after taking Leroy Cudjoe's pass and wrong-footed the Leeds defence to score his 11th try of the season but the champions again struck back straight away, with the captain, Rob Burrow, forcing his way over from dummy half.
Owen then grabbed his second try, Milner forcing his way over from acting half close in, while Ellis also crossed to cap a fine debut.
Michael Claassens, one of the Bath stars yet to re-sign for next year, started the move, linking with Stephen Donald before the fly-half returned the favour with a clever inside ball that left the South Africa scrum-half to force his way over.
