United dominated the opening half, but struggled to find their cutting edge in front of goal against rookie keeper Jamie Jones, who was making his debut for the visitors.
The former Everton youngster had an anxious moment in the early stages when he almost dropped a cross into his own net.
But he recovered well to produce a couple of good saves to deny Scunthorpe's 18-goal leading marksman Gary Hooper.
Orient had little to offer as an attacking force, but almost snatched an unlikely lead when midfield man Jason Demetriou fired a free-kick from the edge of the box straight at goalkeeper Joe Murphy.
It was Scunthorpe who finally made the breakthrough in the 44th minute when a right-wing cross from Martyn Woolford found striker Paul Hayes lurking at the far post to net his 14th goal of the season.
Hooper missed a golden chance to make it 2-0 in the opening minutes of the second half.
Instead it was Orient who found themselves back on level terms in the 59th minute when Ryan Jarvis sent Dean Morgan racing clear to beat Murphy with a confident finish.
Scunthorpe were back in front when winger Garry Thompson grabbed what proved to be the winner, when he curled a delightful shot with the outside of his foot into the far corner past Jones.
Orient threw everything forward to try and force an equaliser but never looked like salvaging a point.
Instead it was Scunthorpe who almost struck again in the 89th minute when Woolford forced his way into the box to get in a shot which beat Jones, only to fall back into the arms of the goalkeeper off the inside of a post.