David Syers swooped to steer in substitute Paul Hayes' cross from the right, helped on by Eddie Nolan's sweeping shot, for Scunthorpe's 79th minute opener.
Substitute Hakeeb Adelakun's stoppage time shot came back off the post and the back of home keeper Jake Cole before trickling in for United's second goal.
Plymouth striker Lewis Alessandra twice hit the post in the second half, curling a shot from the left side of the penalty area on to the far post just a minute after United scored.
Alessandra's close range 62nd minute shot also came back off a post. He reacted quickest to the rebound but sent his shot wide of the opposite upright under pressure from Niall Canavan.
Irish striker Paddy Madden created the best early opportunity of the second half but his 18-yard rising drive was palmed over by keeper Cole.
In the 34th minute Reuben Reid's meandering run down the right carved open a channel and space for onrushing skipper Conor Hourihane, whose first-time left-foot shot from the edge of the box was superbly saved by Scunthorpe keeper Sam Slocombe.