Salford turned in a slick six-try show as Hull KR newcomer Willie Mason finished on the losing side for the first time.
Sean Gleeson celebrated his Salford debut with a touchdown.
Rovers had won the last five meetings against Salford with their only Super League defeat coming in the first clash in 2007.
But the visitors were without injured Clint Newton who had scored in the last three wins over the Reds and saw his run of 67 successive appearances come to an end.
Salford handed ex-Wigan and Wakefield centre Gleeson his debut alongside substitutes Alex Davidson and Callum Marriott.
Reds full-back Luke Patten was relishing the reunion with ex-Canterbury Bulldogs team-mate Mason and came out on top in the private duel.
Salford went close to opening the scoring with both Gleeson and Stephen Wild stopped short and Luke Adamson held up over the line.
Then the Reds produced a mesmerising handling move involving more than half a dozen players for Ryan Boyle to take Daniel Holdsworth’s pass and storm over, Gleeson and Patten also playing crucial roles.
Salford, who had won only one of their five previous games, stretched the advantage to 10-0 with Holdsworth, Matty Smith and Patten combining for Jodie Broughton to squeeze over in the corner.
Holdsworth booted the touchline conversion with Mason finding it difficult to penetrate a stubborn Salford defence after his man-of-the-match performance against Crusaders.
But Rovers clawed back to 10-6 at the break with Blake Green putting Craig Hall over for his second try since his close-season move from Hull.
But Salford finished in style, running in four tries through Stefan Ratchford, Matty Smith, Gleeson and an interception effort from Mark Sneyd.
Salford: Patten, Broughton, Ratchford, Gleeson, Henry, Smith, Holdsworth, Boyle, Godwin, Sidlow, L. Adamson, Nero, Wild. Substitutes: Neal, Sneyd, Marriott, Davidson.
Hull KR: Briscoe, Webster, Hall, Welham, Colbon, Green, Murrell, Wheeldon, Fisher, Watts, Mason, Galea, Netherton. Substitutes: Lovegrove, Clinton, Hodgson, Cockayne.
Referee: J Hewer (RFL).