Northern Ireland international Warren Feeney scored his first goal since the midle of August to earn Bournemouth an injury-time winner.
Feeney struck in the second minute of stoppage time with a low right-foot shot from just inside the area and deflected by Orient captain Dean Smith.
Bournemouth goalkeeper Neil Moss did not have a save to make and it was 87 minutes before Orient forced their only corner.
At the other end Glenn Morris made an outstanding save from Feeney in the 75th minute, diving to his right and in the first half, Wade Elliott went close with a long-range lob which ended on the roof of the net