The visitors almost took the lead within the first five minutes after Scott Cuthbert struck the bar with a header inside the six-yard box.
The opening proceedings were extremely end-to-end, with chances falling to Zeli Ismail and Jobi McAnuff of either side.
Orient began to get a foothold in the match midway through the half and were pumping balls into the County box, but the hosts were defending resiliently.
County then took the lead through Ismail's penalty after Jake Cassidy was fouled in the area after 25 minutes.
McAnuff threatened to pull the visitors level 10 minutes later but Roy Carroll kept the former Reading man out to keep the score 1-0.