Bradford ran rings around their higher-ranked opposition, with former Parramatta Eels full-back Mullaney touching down either side of half-time to help the Bulls build up a sizeable lead and stun his former employers.
Dale Ferguson and Danny Williams had also crossed the whitewash before the Red Devils were even on the board, and despite another former NRL man, Rangi Chase, powering his way over, Bradford were 17-4 up at the break.
And after Mullaney danced around his former club's backline for his second score, the tries kept on coming with Danny Addy, James Clare and Adrian Purtell completing the rout.
Elsewhere, Hull KR prepared for their Challenge Cup final appearance by edging past Widnes Vikings.
In a scrappy all-Super League encounter, it was Australian Josh Mantellato's conversions that ultimately proved the difference in the 12-8 victory.
Hull led just 6-0 at the interval after Kris Welham's score on the stroke of half-time, and after Chris Clarkson's unconverted try, debutant George Lawler pounced on Matthew Marsh's kick to extend Rovers' lead.
But with Matt Whitley dotting down in the final few seconds, it was Mantellato's earlier form with the boot that earned his side the victory as he slotted two goals from two attempts.
And in the final of Sunday's fixtures, Rob Worrincy's hat-trick helped Sheffield Eagles come from behind to snatch a 28-24 victory over Halifax.
A win was vital for both sides after two previous defeats from two encounters each in the qualifiers, and with the scoreline swinging back and forth for most of the clash the result could have gone either way.
Mitch Cahalane ran out for Halifax, but he could not do anything to stop Worrincy grabbing the deciding try just four minutes from time with the scores locked at 24-24, as he touched Patrick Walker's kick down in the corner.
Meanwhile in Saturday's only qualifiers clash, a Lee Smith drop-goal handed Wakefield Trinity Wildcats a 17-16 victory over Leigh Centurions after a thrilling clash.
Full-back Smith may have taken the plaudits having also scored the first try of the game, but it was Jacob Miller's two scores that were the difference which also avenged Wakefield's Challenge Cup exit at the hands of Leigh in May.
Another former NRL man, prop Fuifui Moimoi, had cancelled out Smith's opener with Leigh's first attack of the game, before Jonathan Pownall and Liam Kay put Centurions 16-6 in front.
But Miller produced two sensational darting solo runs in the second half to bring Wakefield storming back.
And the victory -- their second successive win over a Championship team -- hands the Wildcats a massive boost in their hopes of retaining their Super League place for next season.
But a third defeat in three games at the hands of Super League opposition leaves the Centurions with little hope of gaining automatic promotion.