After two matches out with an ankle injury, both of which Leeds lost, Lui linked superbly with half-back partner Luke Gale as Rhinos stormed into a 26-0 interval lead - and also made a vital try-saving tackle.
Salford had a good spell after the break, but Lui scored the try that ended their fightback after they had cut the gap to 14 points and Rhinos finished well on top as Richie Myler and Ash Handley completed fine hat-tricks.
Coach Richard Agar said: "We certainly made some improvements.
"We played very controlled in the first half and found a formula.
"There was some improvements in our contacts and our discipline and certainly in our marker work.
"They are basic things, but when you throw them together they can roll into a better performance.
"And we feel if we get enough of the ball we have got some points in us."
Gale and Liam Sutcliffe - who started at centre in place of hamstring victim Konrad Hurrell - carved out the opening try for Handley after 10 minutes and six later Ryan Lannon could not deal with Gale’s kick and Myler picked up to go over.
Myler returned from injury at full-back which allowed Handley to switch on to the left-wing, with Luke Briscoe dropping out.
In the next set Lui burst through the middle and Gale was in support to cross.
Rhyse Martin converted the second and third tries to make it 16-0 after 18 minutes and Rhinos went close to scoring again soon afterwards, but Liam Sutcliffe lost possession trying to touch down.
Salford went up field in the next set and Chris Atkin dived over at the corner, but referee Liam Moore and video official Ben Thaler ruled he had not got the ball down in Lui’s stunning last-ditch tackle.
That was a big moment as Rhinos scored in their next set. Matt Prior’s superb pass picked out Handley and he kicked infield for Myler to swoop over, Martin again tagging on the two.
Seven minutes before the interval Leeds added their fifth try, Handley getting the ball down after rising to make a fine catch from Gale’s kick.
Niall Evalds pulled a try back off his own kick after 48 minutes and five later he was in again, when Kevin Brown’s kick caught out Myler, Tui Lolohea converting both.
That cut the gap to 14 points, but Lui nipped over from acting-half to calm Leeds’ nerves at the end of the third quarter.
Mikolaj Oledzki had a strong game for Rhinos and grabbed a deserved try with 17 minutes left, accepting Gale’s pass, shrugging off Johnson and giving himself a 30-metre canter to the line.
Martin converted both to end Reds’ brief fightback.
Teenage prop Tom Holroyd had a couple of spells off the bench and was held up over the line eight minutes from time.
Soon afterwards Gale jugged and offloaded to Myler who hacked ahead and ran through to touch down for a freak try and two minutes from the end - after Salford’s only penalty - Liam Sutcliffe picked up Evalds’ kick near Rhinos’ line and handed on to Handley who raced the full length for his hat-trick score.
Martin converted the last two tries to bring up the half-century.
Leeds suffered another injury blow when they lost veteran forward Adam Cuthbertson with a back spasm soon after the interval.
A stretcher was called, but he managed to walk off, in obvious pain. Harry Newman was taken off as a precuation late on after suffering cramp in a hamstring.
Gale made an early try-saving tackle on Ken Sio, who was hurt in the incident - after five minutes - and played no further part, reducing Salford to 16 available players.
They also lost Chris Atkin early in the second half and Josh Johnson in the final quarter.
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