But there was disappointment for the visitors who saw striker Reuben Reid get the ball in the net twice, only to see each effort ruled out.
The game only came to life after the interval following a dour first half in which the only real chance came for Scunthorpe when a close range header from centre-back Niall Canavan was tipped over by keeper Luke McCormick.
It was Plymouth who started the second half stronger with Reid having the ball in the net after 49 minutes, only to be flagged offside.
He went close again 10 minutes later when he stung the fingers of keeper Sam Slocombe with a fiercely struck 25-yard free-kick.
But it was Scunthorpe who finally broke the deadlock in the 62nd minute when Esajas netted his first goal for the club, pouncing from close range after a shot from Sam Winnall had been half-blocked by the visitors' defence.
It perked Scunthorpe into further attacking action and substitute Deon Burton was unlucky to see his close range effort rattle back into play off the underside of the bar.
Plymouth thought they had rescued a point when Reid met a far post cross from Jamie Reckord with a powerful header, only to see it ruled out again for his over-robust aerial challenge on home skipper Andy Dawson.