The two sides were inseperable over the course of the game until the hosts found a way through on spot kicks following penalty misses from Franck Moussa and John Fleck.
City boss Steven Pressley made one enforced change to the side that beat Stevenage away in the league on Saturday, replacing the injured Cyrus Christie with Jordan Willis at right back.
The opening stages gave no great cause for concern for the Sky Blues though as Moses Odubajo and Yohann Lasimant both had efforts at goal in the opening seven minutes, the first seeing Joe Murphy make a comfortable save and the second being blazed high over the bar.
Callum Wilson very nearly carved out a clear cut chance for City after 19 minutes after a sweet series of flicks between Franck Moussa and Leon Clarke ended up at his feet 20 yards out. Wilson then turned Scott Cuthbert with his first touch only to be hauled down on the edge of the area with Moussa's resulting free kick effort going straight into the wall.
It was Cuthbert though who had the only real chance with three minutes of the half to go when a left-sided free kick delivery from Odubajo was whipped into the box, the centre half rising higher than anybody else but guiding his header just over the bar.
The start of the second half was in stark contrast to the first though as both sides had opportunities to find the opener within the first three minutes of the restart, first when a bobbling ball in the Orient area found its way to Leon Clarke who kind find a way through traffic with his shot.
The it was the home side's turn as Lasimant raced up the other end and won a corner, taking it fairly shot to Lloyd James whose first time effort went just wide.
Joe Murphy was required to make the first real save of the game after 54 minutes though when Odubajo burst through the back four and tried to fire into the far bottom corner, only to be denied by a superb reaction stop by the City 'keeper.
Chances again grew few and far between though although the Sky Blues went close twice in the space of two minutes with 17 minutes to go, first when Wilson tried his luck from 20 yards with a dipping effort that flew just over the bar and then when Leon Clarke's free kick effort from a similar distance curl just around the foot of the post.
Orient substitute David Mooney was left with his head in his hands with 13 minutes to go though when a deep floated free kick delivery to the back post found the striker unamrked to head at goal only for Murphy to pull off another great save to keep the scores level.
The battle between Murphy and Mooney then had a second installment with three minutes to go when sub Marvin Bartley let a ball run through to his strike partner who thought his was in on goal only to be surprised by Murphy rushing off his line to make a great save with his legs and then dive on the loose ball as it trickled back into the area.
The game seemed destined for penalties though and in the end the tie was decided from the spot as referee Tim Robinson blew for full time.
All four of Orient's penalty takers in Mooney, Omozusi, Sawyer and James dispatched theirs with ease however City slotting home just two of theirs from Clarke's Leon and Jordan was not enough as the League One leaders went through.
Attendance: 2,151 (489 Sky Blue Army)
Coventry City: Murphy, Willis (Phillips 63), J Clarke, Webster, Adams, Thomas, Barton (Daniels 72), Moussa, Fleck, L Clarke (c), Wilson
Subs: Burge (GK), Manset, Haynes
Leyton Orient: Jones, Omozusi, Sawyer, Vincelot, Cuthbert, James, Odubajo, Batt (Mooney 63), N Clarke (c), Lasimant (Cox 72), Stockley (Bartley 81)
Subs: Larkins (GK), Lee