The Championship part timers gave the Red Devils a fright by sweeping into a 24-12 lead. Salford recovered to lead 34-24 at the break but could never relax and needed a Michael Dobson drop goal to edge ahead 41-34 before sealing victory with two late tries.
Both teams gave Adrian Morley a guard of honour before the kick-off. But the Eagles came close to making it a miserable night for Morley and Salford as they deservedly led 24-12 midway through the first half with tries from Cory Aston, Menzie Yere, the outstanding Quentin Laula-Togagae and Rob Worrincy.
Salford rallied to lead 34-24 at the break with two touchdowns from Josh Griffin and others by Weller Hauraki, Harrison Hansen, Liam Hood and Lama Tasi.
However, Sheffield did not give up and added second half tries through Duane Straugheir and Scott Turner to trail 40-34.
Salford needed a Dobson drop-goal on his 200th British appearance to calm the nerves before Iain Thornley and George Griffin crossed for late tries after Thornley had set another up for Niall Evalds.
Eagles coach Mark Aston was full of praise for his side’s effort but said: “I’m gutted we lost because I really believed we could come here and win.
“The final scoreline flattered Salford and they were probably a bit surprised at the amount of football we had in us.
“We really challenged them to do the unexpected and I was pleased offensively - but we let in some soft tries.
“If we had smartened up a bit we could have won. We certainly didn’t come here to lose. We completed at 90 per cent in the second half but the end of our sets were poor.”
Salford: Evalds, Jones-Bishop, Thornley, J. Griffin, Johnson, Lee, Dobson, G. Griffin, Tomkins, Taylor, Hansen, Maitua, Hauraki. Substitutes: Hood, Forster, Tasi, Morley.
Sheffield: Laulu-Togagae, Turner, Yere, Smeaton, Worrincy, Brambani, Aston, Battye, Carlile, Stringer, Knowles, Straughier, Walker. Substitutes: Taulapapa, Petersen, Davey, Scott.
Referee: G Hewer (RFL).