Chris Ashton and Pat Richards put the result beyond doubt while Barrett fed Mark Calderwood for Wigan's fifth try.
Mark Flanagan brought Wigan back into it with a try but the Giants started to pile the pressure on the visitors and David Hodgson capitalised before Lunt went over for the first of his scores.
"The game will be the first opportunity for our supporters to see Mark Riddell in a Wigan shirt, and Karl Pryce is now fully fit and raring to play, " said Wigan coach Brian Noble.
But further tries from Mark Calderwood and Sean O'Loughlin helped Wigan into the last four.
Barnett pulled one back for the Eagles with his second try, to which Tomkins responded with a third try, Richards adding the extras to take Wigan to the 50-point mark.
Quins, who gave debuts to former England winger Mark Calderwood and 20-year-old Wigan trialist half-back Joe Mellor, seized control with those two early tries and never looked like relinquishing their hold.
Wigan were then punished Australian wing Mark Lennon made a decisive break down the left, found Lupton who put scrum-half Van Dijk on a 20-yard run under the posts for Lennon to convert.
Captain Mark Smith, who won a Challenge Cup with Wigan in 2002, was among a host of Vikings ruled out through injury, while Paul Cullen was unable to call on four dual-registration players including Wigan trio Shaun Ainscough, Liam Farrell and Ben Davies.
Maik Taylor (Fulham), Roy Carroll (Wigan), Aaron Hughes (Newcastle), Mark Williams (Watford), Danny Griffin (St Johnstone), Ian Nolan (Sheffield Wednesday), Colin Murdock (Preston), Pat McGibbon (Wigan), Kevin Horlock (Manchester City), Keith Gillespie (Blackburn), Damien Johnson (Blackburn), Michael Hughes (Wimbledon), Jim Magilton (Ipswich), Jeff Whitley (Manchester City), Danny Sonner (Sheffield Wednesday), Steve Lomas (West Ham), James Quinn (West Brom), Adrian Coote (Norwich), David Healy (Manchester United), Stephen Robinson (Bournemouth).
Barrett's denial follows Wigan coach Brian Noble insisting the stories were wide of the mark.
Mark Dalle Cort's unconverted try made it 16-6 but Wigan were level through Cameron Phelps and Amos Roberts.
Former Manchester City boss Mark Hughes, Stoke assistant boss Peter Reid, former Peterborough coach Darren Ferguson, ex-Wigan manager Paul Jewell and former West Ham boss Alan Curbishley have also been suggested as possible candidates.
Wigan coach Michael Maguire resisted any temptation to include fit-again Amos Roberts, while leaving Mark Riddell on the bench.
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