Australian centre Moon was snapped up by Leeds following an impressive season with the Reds last year - he scored 11 tries in 19 games - and touched down twice as part of a classy display.
He was not always joined in excellence by his team-mates as Salford occasionally made life difficult for Brian McDermott's reigning champions, but the Rhinos had enough about them to pull clear when they needed to.
Full-back Zak Hardaker - concussed in last week's defeat at Castleford - went off at half-time with suggestions circulating he was being given a cautionary breather, and he will head McDermott's injury checklist, along with Ryan Bailey, Brett Delaney and Jamie Peacock, who sat out entirely.
With three of their leading lights missing, Leeds chose to allow Kylie Leuluai, Richard Moore and Stevie Ward to audition for a World Club Challenge shirt, and the latter submitted a third-minute try as part of his case, winning a footrace to score.
Having survived a spell from Salford, Leeds duly scored their second try, Moon getting his first when he was quicker than team-mates Carl Ablett and Kevin Sinfield to get to Danny McGuire's kick. Leeds picked up a third score with 26 minutes gone as Kallum Watkins finished off a neat right-side move that was started by Ian Kirke's barging run.
Moon then appeared to have forgotten he had left Salford as he twice knocked on when looking to ground the ball over the line, before the visitors unexpectedly got on the scoreboard with seconds of the first half left. Ashley Gibson ran on to Marc Sneyd's kick to score after good work from Jodie Broughton.
Sneyd kicked the goal and was lining another up three minutes after the restart when Niall Evalds, Salford's scorer in France last week, snapped up an intercept off McGuire and went the length of the field. The conversion was missed, leaving the score at 18-10, and there were suggestions Salford had a chance.
But Leeds quickly flexed their muscles to show who was in charge, with their two-in-four-minutes spell kickstarted by the introduction of hooker Paul McShane. He had a hand in the move which gave Moon his second 49 minutes in and then dug his way over the line twice.
Salford then thought they had grabbed the last word when Gibson poached a second, but Sinfield had that honour, scoring a try after Adam Neal's loose pass, before kicking his seventh goal, extending his 100 per cent record for the year to 15.