Saints led by just four points at the interval but Hunslet's resistance faded when the Super League visitors added five of their eight tries with Paul Sculthorpe using his finishing strength to get two of them.
Bradford Bulls chalked up a club record 92-0 win at Workington to stroll into the last 16, where they face a trip to Wakefield Trinity. It was also a record defeat for the First Division Cumbrians, who were already trailing 14-0 by the time second-row forward Barry Williams was sent off after 18 minutes for allegedly kicking out at Robbie Paul.
A hopeless task then became impossible and the Bulls underlined their Super League class to score 17 tries, with their new Australian recruit Michael Withers and the former Salford centre Nathan McAvoy scoring four apiece.
Warrington turned on the style to secure a home tie with Halifax courtesy of a resounding 50-6 win over Featherstone Rovers at Wilderspool.
Winger Mark Forster's hat-trick was upstaged by one from new signing Alan Hunte, who grabbed his in a late eight-minute burst.
Huddersfield Giants, bottom of Super League last season, enjoyed a 14- try romp against Swinton at McAlpine Stadium. Craig Weston grabbed a first- half hat-trick and he was aided by Paul Cook (2), Paul Loughlin, Bobbie Goulding, Danny Arnold and Dave Broughton, who all crossed in an embarrassingly one-sided first 40 minutes as the Giants, under new coach Mal Reilly, eventually cruised to a 78-4 win.
Rob Smyth kicked 10 conversions from 11 attempts as the London Broncos strolled to a 64-0 triumph over Doncaster at The Stoop to earn a trip to Hull KR. Karle Hammond led the way with a hat-trick on his debut.
Leeds v St Helens
Widnes v Leigh
Hull KR v London
Castleford v York
Wakefield v Bradford
Huddersfield v Salford
Warrington v Halifax
Whitehaven v Oldham or
Ties to be played on 27-28 February.