Ash Hunter spoiled Barrow fans’ Holker Street homecoming as he scored the only goal in a 1-0 win for Salford.
Over 800 supporters returned to see the hosts play in the Football League for the first time since 1972.
All seven of Barrow’s league defeats have been to a solitary goal.
Salford goalkeeper Vaclav Hladky pulled off a string of fine saves to frustrate David Dunn’s men, and Hunter’s 48th-minute cross-shot secured all three points for Richie Wellens’ visitors.
Barrow dominated the first half, with Jason Lowe’s audacious 30-yard effort the only sight of goal for the Ammies.
Scott Quigley was kept out by Hladky before the keeper again denied him with a superb one-handed stop from a 20-yard effort.
Hladky frustrated Quigley once again in first-half stoppage time before the returning Jayden Reid missed the rebound.
Against the run of play, Hunter’s effort nestled in off the post just after the break.
Luke James failed to hit the target with a great chance to equalise after the break before Reid was kept out by Hladky.
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