Kallum Watkins scored a brace of touchdowns and skipper Kevin Sinfield kicked seven goals from as many attempts for the Rhinos who have now won 10 consecutive clashes against the City Reds since their shock Headingley defeat in 2009.
Elliot Minchella, a 17-year-old back-rower, also marked his debut with the final try after coming off the bench. But Leeds lost centre Jimmy Keinhorst with a dislocated shoulder after Ryan Hall pulled out before the kick off through illness.
McDermott said: "We faced a resilient Salford and had to fight hard.
"The scoreline flattered us a bit and we scored a few long-range tries but you have to credit Salford's tenacity. They wouldn't go away."
McDermott singled out Minchella, saying: "He's been a stand-out performer in the Under-19s this season and showed up well. It was nice for him to score a try.
"But it's a real shame for Jimmy who goes into our injury room with the others."
Salford replied with tries from Ashley Gibson - against his old club - Lee Gaskell and Theo Fages.
"I can't fault my players and the scoreline did flatter Leeds," said boss Brian Noble.
"But they counter-punched really well and their super players turned up when they were needed.
"Some of our young kids were given time and showed real promise. Will Hope has had a bad shoulder all year but did well and Niall Evalds toiled hard.
"Jordan Davies showed glimpses in the centre of what he may be able to do but our best player was Stephen Wild who led the team really well. The fans got behind us and they sensed the players commitment and effort."