Goalkeeper David Stockdale, on loan from Fulham, kept the visitors in the game in the early stages with two good saves.
He kept out a well-struck effort from Sam Togwell before turning away a shot from Grant McCann.
But it was Plymouth that snatched the lead after 28 minutes when winger Yannick Bolasie got free on the left and fired in a low cross which striker Jamie Mackie turned in at the far post for his ninth goal of the season.
But four minutes later Scunthorpe were back on level terms from a well-worked free-kick routine which saw Paul Hayes pull the ball back low into the middle for Garry Thompson to apply the finishing touch.
The hard-working Thompson nearly struck again just before the interval when he got free inside the box only to be denied by another fine Stockdale save.
Thompson wasted another good opening as Scunthorpe searched for the lead in a tense, scrappy affair.
It was Plymouth who nearly went back in front on the hour with a cracking effort from Chris Clark that was kept out by keeper Joe Murphy.
But five minutes later Scunthorpe made it 2-1 when winger Martyn Woolford cut in from the right to try his luck with a left-foot shot that took a deflection as it curled past Stockdale and into the far corner.
Striker Paul Hayes then had a chance to make things safe for Scunthorpe but his close range effort was kept out by that man Stockdale.
In the closing minutes Bolasie missed a great chance to grab an equaliser for Argyle when he miscued in front of goal, while at the other end substitute Jonathan Forte missed a couple of good chances for Scunthorpe.