Salford ground out their fifth successive win and condemned the Centurions to a fourth defeat in a row in the Good Friday derby at the AJ Bell Stadium.
Fullback Gareth O’Brien was the home hero, slicking through to score the decisive try down the right with 13 minutes remaining, Michael Dobson adding the angled conversion.
Leigh had defended heroically in the wet conditions but after conceding back-to-back repeat sets their brave second half resistance was finally broken.
Leigh Centurions Head Coach Neil Jukes said: “We worked hard and our attitude and effort was good but two individual errors cost us, one missed tackle on our left and a slip for their second try.
“I thought defensively to keep a good attacking side like Salford to the score we did, especially on the back of a poor completion rate, was good.
“But we need to create more pressure than we did today. We need to complete a lot higher to give ourselves an opportunity.
“The kicking game of Salford’s halves and their game management was superior.”
Salford Head Coach Ian Watson said: ” “We have talked about being resilient and coming through close games and we showed that again today.
“Last season we were involved in a lot of close games and just didn’t quite get there. We won’t get carried away with winning five games in a row.
“I thought Leigh were great and they turned up here and had a real dig. They are an aggressive team but our middles stood up to them pretty well.
“In the first half we were a little bit off but in the second we controlled the game really well on the back of Michael Dobson’s kicking game, which is what we wanted to do in the conditions.”
O’Brien had given the home side the lead with a penalty but Mitch Brown fastened onto a Martyn Ridyard grubber-kick to score, Ben Reynolds converting.
Kris Welham sent his side in at the interval on level terms after capitalising on a missed tackle out wide.
Brown was taken off with a head injury late in the first half that will also rule him out of Easter Monday’s home game against Hull FC.
And several other players joined Leigh’s list of walking wounded.
“We will patch ourselves up and go again Monday,” Jukes added. “We worked hard to get into Super League and we’ll be ready to go.”
Salford Red Devils: Gareth O’Brien; Greg Johnson, Kris Welham, Junior Sa’u, Justin Carney; Rob Lui, Michael Dobson (captain); Lama Tasi, Logan Tomkins, Lee Mossop, Josh Jones, Ben Murdoch-Lasila, Mark Flanagan. Interchange: Craig Kopczak, George Griffin, Josh Wood, Adam Waine.
Tries: Welham (38), O’Brien (67)
Goals: O’Brien 1/ 1, Dobson 1/ 2.
Leigh Centurions: Gregg McNally; Adam Higson, Ben Crooks, Mitch Brown, Matty Dawson; Ben Reynolds, Martyn Ridyard; Jamie Acton, Micky Higham (captain), Danny Tickle, Atelea Vea, Glenn Stewart, Harrison Hansen. Interchange: Eloi Pellissier, Dayne Weston, Sam Hopkins, Lachlan Burr.
Try: Brown (28); Goals: Reynolds 1/ 1.
Referee: Jack Smith.