The visitors received an early blow when Reda Johnson, an injury doubt in the build-up to the game, was forced to withdraw after only eight minutes.
However, the Sky Blues almost took the lead after a quarter of an hour when Frank Nouble, a scorer in their 3-2 win against Peterborough United last weekend, was afforded space by the Orient defence only to see his shot blocked.
City, who started the game two places ahead of their opponents in the League One table, continued to press forward and had another chance to score through loanee Gary Madine, but his header failed to trouble Gary Woods in the home side's goal.
Madine again threatened to forge a breakthrough on 28 minutes. However, Orient's defence were able to block his strike.
Their pressure finally told on 35 minutes when O'Brien fired the ball into the top corner of Woods's net after being teed up by Madine.