Kallum Cesay’s winner completed a five-goal thriller to bring Salford level with Swindon on points.
Ryan Graydon should have opened the scoring with a near-post header but glanced across the face of the Town goal from Luke Garbutt’s cross.
Oliver Turton made no mistake with a glancing header from Garbutt‘s corner to put the Ammies ahead in the 24th minute.
Seven minutes later a patient build-up saw Graydon tee up Kelly N’Mai in the box to notch.
But Town halved the deficit as Joel McGregor’s deft near-post header dropped in at the far post.
Salford’s Jorge Grant then hit the crossbar with his inswinging corner.
When Connor Ripley botched a clearance after rushing out of his box, Graydon fluffed a golden chance to restore the two-goal cushion.
After the break, Matthew Young punched away a Gavin Kilkenny effort from outside the box.
Salford made it three in the 72nd minute when Daniel Udoh squared for Cesay to tuck away.
Aaron Drinan’s header from Fletcher Holman’s cross gave Town hope but City held on.
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