The home side dominated much of a goalless first half, without being able to make the breakthrough.
The nearest they came was after 15 minutes when midfielder Josh Walker, making his home debut on loan from Watford, tried his luck with a a shot from the edge of the box which was fingertipped over at full stretch by keeper Chris Day.
Stevenage came into the game just before the interval, Luke Freeman missing a great chance to open the scoring when he lifted his shot over with the goal at his mercy after a rampaging run down the right by Lawrie Wilson.
Michael Bostwick should also have done better when he volleyed wide at the far post from a corner.
But it was Scunthorpe who took the lead two minutes into the second half when a ball over the top of the visitors' defence sent striker Garry Thompson racing through the middle to hammer a right-foot shot past Day for only his second goal of the season.
But with only six minute remaining the home defence failed to clear a cross from the right and substitute Darius Charles turned to squeeze a close-range shot past keeper Sam Slocombe as Scunthorpe had to settle for their 13th draw of the campaign.