Robertson blazed clear to set up the try of the night for teammate and former Brisbane Bronco Tristan Sailor before the Australian returned the favour with a neat kick to send the youngster over to seal the Saints' win.
An early try from ex-North Queensland Cowboy Kyle Feldt gave the Saints a 6-2 half-time advantage with Jake Connor's kick all the Rhinos had to show for their efforts in the opening period.
Jeff Whitley also scored after the break as Paul Wellens' men moved 20 points clear before a late Leeds rally, with both Ash Handley and Harry Newman crossing.
Salford came on strong in the second half to sink Championship side Bradford and book their place in the last eight with a 26-16 victory.
Paul Rowley's men, who lost star half-back Marc Sneyd to Warrington this week, must have feared the worst when Kieran Gill skipped clear to give the visitors the lead.
But late tries from Jayden Nikorima and Ethan Ryan, coupled with 10 points from the boot of Sneyd's replacement Kai Morgan, gave the hosts some welcome relief from their ongoing financial plight.
A back-to-back brace from Guy Armitage and Zac Fulton, grandson of late NRL Immortal Bob Fulton, had given Bradford the initiative after Esan Marsters' early try for the hosts.
But after reaching half-time four points adrift, Salford reclaimed the lead when Ryan Brierley went over and bounced back after Gill's break to ultimately seal victory with relative ease.
Oliver Gildart scored two of seven Hull KR tries as Willie Peters' men cruised to a 40-0 success over Championship side Oldham at Sewell Group Craven Park.
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