Kallum Watkins scored two touchdowns and skipper Kevin Sinfield kicked seven goals as many seven attempts for the Rhinos who have now won the last 10 clashes against the City Reds since their shock Headingley defeat in 2009.
Leeds centre Joel Moon missed the clash against his old club through a foot injury with the Rhinos also without Brett Delaney, Stevie Ward, Danny McGuire, Jamie Jones-Buchanan and Ryan Bailey.
Ryan Hall also pulled out just before the kick-off through sickness with Liam Sutcliffe switched to the wing and Alex Foster drafted in as a late sub.
The Rhinos handed 17-year-old Elliot Minchella his debut off the bench - the sixth Academy player to make his bow this year - and the teenager notched the final try five minutes from time.
Leeds included 13 players who came through their youth system with Kylie Leuluai the only import on duty.
Salford welcomed back Lee Jewitt and Jake Emmitt from suspension but ex-Leeds prop Darrell Griffin was still banned with skipper Martin Gleeson, Jodie Broughton, Lee Jewitt, Matty Ashurst and Wayne Godwin injured.
The Reds made a lively start and harassed Leeds into mistakes but a Lee Gaskell kick was too long to worry the defence.
Sutcliffe was bundled into touch by determined tackling on the Rhinos' first raid but Leeds went ahead after 19 minutes when Rob Burrow sent Sutcliffe away and Watkins touched down in the corner.
Sinfield booted the conversion and also added the extras to Zak Hardaker's touchdown four minutes later after the full-back was put clear by Watkins. Hardaker left Gaskell flat-footed on a 40-metre weaving run to the line.
But Salford were rewarded for their efforts when Ashley Gibson latched onto Theo Fages' kick to score against his old club with Marc Sneyd adding the conversion to cut the gap to 12-6.
The Reds' joy was short-lived with Burrow scooting 35 metres for a trademark solo try and Sinfield landing his third goal.
Burrow was the provider for Carl Ablett's try after 35 minutes with a perfectly-timed pass to stretch the lead to 24-6 at the break.
Salford's defence crumbled early in the second half with Ablett bursting through several weak tackles for Ben Jones-Bishop to cross.
But neat work from Fages allowed Gaskell to round Hardaker for a fine try to leave Salford trailing 30-10.
Watkins supported Sutcliffe's breakaway to grab the Rhinos' sixth touchdown after 64 minutes.
Leeds lost centre Jimmy Keinhorst 10 minutes from time with an arm injury before Fages made the scoreline more respectable with a try converted by Gaskell.
Then Minchella marked his bow in style with a try to wrap up the win.