David Mooney, Elliott Omozusi, Gary Sawyer and Lloyd James netted their spot-kicks for the home side and although Leon Clarke and Jordan Clarke were on target in reply for the Sky Blues, Franck Moussa had his effort saved by Jamie Jones while John Fleck missed the target.
In a dour first 45 minutes neither goalkeeper was called into serious action as defences ruled the roost in a half that will not stay long in the memory.
The best chance fell to Orient centre-back Scott Cuthbert, who ran on to meet James' free-kick but sent his header over the crossbar from close range.
The second half was a livelier affair with the best chance falling to substitute Mooney two minutes from the end of normal time.
Sent clear by Dean Cox, the striker attempted to round Joe Murphy but the Sky Blues goalkeeper extended himself to dive at the feet of Mooney and clear the danger.
The visitors' best effort came courtesy of Leon Clarke's 25-yard free-kick which flew inches wide of a post.