An own goal from Jean-Yves M'Voto, a Jack King strike just after the break and a late third from Hakeeb Adelakun won the game for the Iron, who will now face Chelsea in the next round.
The Iron made two changes from the 1-1 draw at Port Vale - alerations which saw Jamie Ness replace the cup-tied Tommy Rowe and Kyle Wootton come in for Dutchman Kevin van Veen. This meant nine kept their place in the side. Luke Daniels started inbetween the sticks, and in front of him was an unchanged back four of Scott Wiseman, Niall Canavan, Charlie Goode and Scott Laird.
Neal Bishop played alongside King and Ness in the heart of the United midfield, and ahead of them was a front three of Paddy Madden, Luke Williams, and Wootton.
United made a positive start to the match, and registered the first effort on target through Wootton, two minutes in. After some neat build up play down the right hand side, the ball was hung up for the frontman, who guided his downward header into the arms of O's 'keeper Alex Cisak.
The Iron survived a scare in the 10th minute when Bradley Pritchard struck the post with a deflected effort. After a spell of pinball in the penalty area, the ball fell to the midfielder, whose strike was diverted onto the post by Goode's outstretched leg.
Williams then went close for Mark Robins' side, with a close range free-kick. It had been down to some good inter-play between Madden and Wootton on the edge of the box which gave the former Middlesbrough man the opportunity. However, despite the favourable position in which the ball was situated, he saw his effort trickle out for a corner kick.
The chances were coming thick and fast for both sides, and it was the turn of the visitors to try and break the deadlock next. Defender M'Voto found himself free in the Iron penalty area, but in spite of this, he could only direct his header high and over the crossbar.
A second headed opportunity came the way of Orient soon after. This time it was Mathieu Baudry who tried his luck, and unlike M'Voto before him, he did test Daniels. The effort drew a good save out of the Iron stopper, who palmed the header over the bar.
It was a frustrating half for the Iron, who struggled to break down a resilient Orient defence.
Robins' men were keen to stamp their authority on the second period, and this was evident as they pressed right from the kick off.
Two minutes after play resumed, the ball found it's way to full-back Laird, who fired just over from a tight angle, after some good link-up play between Wootton and Madden.
The home side then went close once more when King flashed a header over from close range. The midfielder created some space for himself, but could only direct Williams' corner into the Iron fans behind the goal.
United's endevour was rewarded though, ten minutes into the second period. After some hesitancy in the Orient backline, Williams picked up a loose ball and found Bishop with an incisive pass. The midfielder didn't make the best of contact with the ball, but fortunately enough, the ball was diverted into Cisak's net via defender M'Voto.
And after making the crucial breakthrough, United then doubled their advantage five minutes later. Williams once again was the instigator for the home side, as he delivered a superbly flighted corner into the six yard area. Then after a goalmouth scramble, King poked home from a yard out, to put the Iron in a commanding position.
The second goal really took the wind out of the visitors' sails, and the Iron were able to dominate the ball in the closing stages.
There were opportunities to add a little more gloss to the scoreline, and it looked as though United would have to settle for two, but substitute Adelakun added a third and sealed the victory in the closing stages with a close range finish, after being found by Williams.
The Glanford Park faithful were clearly delighted at the full-time whistle, as their side will now face Chelsea in a mouthwatering clash at Stamford Bridge in the new year.
Scunthorpe United: Daniels, Wiseman, Laird, Canavan, Williams, Madden, Bishop, King, Goode, Ness (McAllister 78), Wootton (Adelakun 83).
Substitutes not used: Anyon, van Veen, Henderson, Boyce, Clarke.
Leyton Orient: Cisak, Clohessy, Shaw, Baudry, James (Turgott 62), Palmer (Marquis 62), McAnuff (Adeboyejo 71), Payne, M'Voto, Pritchard, Simpson.
Substitutes not used: Grainger, Essam, Dunne, Kashket.