Paul Wellens grabbed two tries to help Saints climb to the top of the Super League.
But the victory came despite injuries to Jon Wilkin, Tommy Makinson and a dazed Anthony Walker.
After a stop-start opening 15 minutes Saints hit the front when the rejuvenated Wellens cashed in on a big drive from Mose Masoe to force his way over.
Salford enjoyed a strong period of pressure, but Saints held out and countered with a quick-fire brace of tries.
First Sia Soliola powered through a three man tackle to grab the first of those with Saints punishing an indiscretion by Gareth Hock.
And then Lance Hohaia dashed in after a break from Jon Wilkin.
Unfortuantely that was Wilkin’s last contribution and he was led off shortly afterwards holding his arm.
Salford wing Niall Evalds was first on the second half scoresheet when he reacted quickest to Rangi Chase’s smart grubber.
But that was swiftly cancelled out by an opportunistic effort from the fleet-footed Gary Wheeler, who backed up last week's two try effort.
And Wellens showed that he has not lost that scoring knack when he linked up to cross the line, rendering Hock's late score only a mere consolation.
Walsh missed just one conversion and completed the scoring with the second of two late penalties.