Super substitute James Wilson scored a brace on his Salford debut but it was not enough as Ryan Hardie's stoppage-time strike earned Plymouth a narrow 3-2 Sky Bet League Two win.
Win £250,000 on Tuesday!
FREE TO PLAY: Do not miss your chance to land the Super 6 jackpot for the sixth time this season on Tuesday.
Hardie darted clear down the right before firing home low into the corner at the end of a thrilling clash.
Salford's Ash Hunter twice went close in the early stages.
He dragged an angled effort inches wide, then lashed in a strike from 25 yards that was also just off target.
Plymouth went in front after 18 minutes. Antoni Sarcevic clipped in a cross and though Byron Moore scuffed an initial effort, he made no mistake the second time as he tapped home from four yards.
Salford responded with Bruno Andrade firing narrowly wide following a neat lay-off from Adam Rooney.
Salford goalkeeper Kyle Letheren twice saved the hosts early in the second half, keeping out great strikes from George Cooper and Sarcevic.
Wilson levelled with his first touch after coming on as he glanced home a looping header only for Argyle to swiftly retake the lead as Sarcevic curled home brilliantly from 25 yards.
However, Wilson struck again two minutes later, turning sweetly before firing home from 15 yards, while Hardie's late winner settled matters.