Tries from Paul Rowley and John Duffy helped Leigh keep Salford in check on 10-10 at the break.
But Salford looked brighter after the restart when centre Stuart Littler touched down.
Winger Steve Maden's try kept Leigh's hopes alive late on but a try for Anthony Stewart in the closing stages sealed the win for Salford.
Salford coach Karl Harrison: "Next season starts tomorrow. We have already signed our 25-man squad for and we are well on our way.
"I thought Leigh played really well. They had a game plan and stuck to it and made it difficult for us.
"The forwards had a lot of defending to do and our big guys stood up in what was a physical encounter."
Leigh: Wilshere, Maden, Jackson, Cooper, Owen, Forber, J. Duffy, Fleary, Rowley, Sturm, Stapleton, Leafa, Kent.
Replacements: Wilkes, Marshall, Stevens, J. Duffy.
Salford: Fitzpatrick, Langi, Stewart, Littler, Hodgson, Beverley, Robinson, Coley, Alker, Highton, Brocklehurst, Shipway, Charles.
Replacements: McAvoy, Baldwin, Haggerty, Rutgerson.
Referee: Richard Silverwood (Dewsbury)