Rhinos won only one of their final 11 league matches and will be in real danger of relegation when they go into the Qualifiers if they do not improve.
Rhinos went ahead after 70 seconds when Brad Dwyer forced his way over, but were 22-6 behind at the end of the first half.
Ryan Lannon and Niall Evalds scored back-to-back tries, then new signing from Manly Jackson Hastings touched down before Ed Chamberlain sliced through and kicked his third conversion.
Salford prop Lee Mossop was sent off for butting Rhinos captain Carl Ablett and the penalty led to a try for Liam Sutcliffe who added his second conversion.
On the final play of the half outstanding stand-off Robert Lui strolled over from close range to leave Leeds with a mountain to climb.
Tom Briscoe pulled a try back for Leeds in the third quarter, but Evalds’s second touchdown and a Josh Jones try, both improved by Chamberlain, made it 38-16 before Matt Parcell grabbed a late consolation and Sutcliffe’s goal completed the scoring.
Disappointed Rhinos boss Kevin Sinfield pulled no punches. He admitted his side were totally outplayed by their second-bottom opponents.
The director of rugby had been encouraged by Rhinos’ previous two performances and he said: “I think we’ve made some strides, but clearly not enough.
“It was a big setback, there’s a lot for us to fix up and we will do.”
Sinfield continued: “It was never going to be easy, this one. I thought we did some good stuff last week, but clearly not good enough [last night]. We were clearly outplayed by 12 men.
“I thought Jackson Hastings had a great first 20 minutes, he won the game for Salford.
“On the back of that Robert Lui kicked the ball out, slowed the game down and managed the game and unfortunately we’re not capable of dealing with that at the moment. We can throw our teddies out of the pram or we can try so something about it, which is what we’ll do.”
Forwards Carl Ablett (ankle) and Mitch Garbutt (knee) both picked up injuries.”
Salford: Evalds, Bibby, Chamberlain, Sa’u, Olpherts, Lui, Hastings, Mossop, Wood, Murray, Jones, McCarthy, Lannon. Substitutes: Bennion, Flanagan, Tasi, Nakubuwai.
Leeds Rhinos: Golding, T. Briscoe, Keinhorst, Handley, L. Briscoe, Moon, L. Sutcliffe, Garbutt, Dwyer, Singleton, Ablett, Thompson, Smith. Substitutes: Parcell, Peteru, Walters, Crosby.
Referee: Tom Grant (RFL).