Gary Madine then squandered two chances to put Steven Pressley's ahead before teeing up O'Brien on 35 minutes, and the midfielder smashed the ball beyond the reach of Gary Woods to give the away side a half-time advantage.
However, the O's were much improved after the break and got back on level terms in the 54th minute when Scott Cuthbert nodded Dean Cox's cross past Coventry keeper Lee Burge.
Orient then took the lead with 20 minutes remaining as Jay Simpson headed Mathieu Baudry's pinpoint cross into the roof of the net to put the Londoners within sight of a first home league win of the season.
However, they were denied in injury time when O'Brien tucked the ball into the bottom corner. The draw sees both sides drop closer to the League One relegation zone.