Two tries from Jason Roach early in the second half settled it, but before and after that Salford showed a willingness to fight back that left their coach, Andy Gregory, in a relatively upbeat mood.
In the opening minutes, they were on the way to another humiliation with well-crafted tries from Lee Penny and Toa Kohe-Love putting Warrington eight points up.
Salford's initial fightback began with a mistake by Roach, when he carried a kick into touch.
A clever inside ball from Bobby Thompson put Malcolm Alker over for the try and with that Salford's self-belief was back.
Shortly before half-time, a fine run from the dangerous Thompson set up the position from which Carl Briggs wormed his way over, Steve Blakeley's conversion producing an unlikely half-time lead.
Warrington should have wiped that out when Penny made an incisive break only to throw his pass behind Alan Hunte. They did not have long to wait, Ian Knott lobbing out the pass for the first of Roach's touchdowns.
Danny Farrar provided the ball for the second as Salford were again caught on the blindside and when Michael Wainwright set up Mark Forster, and Lee Briers landed his third conversion of the half, Warrington again looked capable of running away with it.
But then the best move of the match, initiated by Scott Martin and Gary Broadbent, yielded Alker's second try and David Hulme's last-minute effort, also converted, made the result look closer than it was.
Warrington's Darryl Van de Velde was sufficiently nervous to watch the last few minutes from the touchline, even though he knew Salford would run out of time.
For Gregory, a measure of pride in the wholehearted effort of his side has to be tempered by concern over where any actual wins are coming from.
"We fought back," he said. "But if you let in 26 points, you aren't going to win many games."
nSalford have signed Chris Morley, the Welsh international forward, on a one-year contract. Morley, aged 25, the former St Helens and Warrington Wolves player, has impressed in two reserve trial matches before his debut yesterday. He is the elder brother of the Leeds Rhinos forward, Adrian.
Salford Reds: Broadbent; Thompson, Littler, Casey, Carige; Blakeley, Briggs; Southern, Alker, Baynes, Highton, J Faimalo, Hulme. Substitutes used: Crompton, Martin, Bradbury, Morley.
Warrington Wolves: Penny; Roach, Kohe-Love, Hunte, Forster; Wilson, Briers; Hilton, Farrar, Nutley, Gillies, Knott, Roper. Substitutes used: McCurrie, Chambers, Wainwright.
Referee: R Connolly (Wigan).
nDarren Turner marked his return from a six-match suspension with the try which brought Sheffield Eagles their first win of 1999, a 32-28 victory over Huddersfield. The Eagles were clinging to a 25-22 lead when `Rocky' Turner forced his way over from close range for his side's fifth try.