Rovers scored in the first minute, but were 20-6 down before they next had possession.
Salford’s huge win keeps alive their hopes of overhauling Huddersfield Giants and Hull KR on the Qualifiers table and avoiding the million pound match.
The Championship part-timers stunned Salford with the opening try, scored by Jordan Baldwinson after Anthony Thackery’s initial break had been supported by Misi Taulapapa and Andy Ellis.
Kyle Briggs converted, but Taulapapa dropped the re-start and Salford scored successive tries through Weller Hauraki, Junior Sa’u, Josh Jones and Daniel Vidot.
Rovers got their hands on the ball when Luke Briscoe caught a high kick, but he knocked-on and Sa’u took advantage to scored his second.
Jack Ormondroyd touched down from a kick by Briggs, who converted, but Salford added further tries by Niall Evalds, Ben Murdoch-Masila and Logan Tomkins to go in at the break 44-16 ahead.
Josh Walters crossed for Rovers at the start of the second half, but Salford dominated after that with Olsi Krasniqi, Hauraki, Michael Dobson, Murdoch-Masila and Jones all going over.
Gareth O’Brien kicked nine goals from 12 attempts and Robert Lui failed to convert the hosts’ final try.