It was a terrible afternoon for the top two in Super League, Warrington and Huddersfield both beaten by teams near the bottom.
Wolves, who beat Salford 60-0 the last time they met, had six players backing up from the Headingley game on Friday, but still looked to be on their way when they led 10-6.
Salford sensed their chance, however, and took the lead through tries from Luke Patten and Mark Henry.
Warrington got one back from Salford's old boy Richie Myler, but the City Reds clung on for an improbable 18-16 victory.
The Giants had similar problems at struggling Wakefield. With Danny Brough injured and David Faiumu and David Fa'alogo rested, they fell behind 10-0 with Luke George scoring the Wildcats' try. Huddersfield came back with tries by Shaun Lunt and Joe Wardle, but Wakefield edged home 13-10.
There were no such dramas at the KC Stadium, where Hull were routine 38-6 winners over Harlequins.
In Saturday's only game, the Catalan Dragons maintained their play-off momentum with a 31-18 home win over Crusaders. Two tries from Damien Blanch helped to break down the Welsh side's stubborn resistance.Reuse content