The visitors made a bright start to the match and caused early problems with their set pieces, Lewis Grabban coming closest when he fired a shot over following a corner.
Hamer was called upon again in the 22nd minute when he did well to narrow the angle when Grabban looked to be in a promising position, eventually winning his side a goal kick.
Charlton almost opened the scoring shortly afterwards as Danny Green cut inside from the left flank before firing an effort towards goal that Lee Camp failed to deal with at the first attempt. Simon Church was in close attendance, but the Bournemouth keeper recovered in time to gather.
Camp was beaten five minutes before half time as Green and Johnnie Jackson linked up well before the latter fired an effort towards goal, only to see his strike come back off the post.
The hosts continued to threaten in the closing stages of the half and almost broke the deadlock in the 44th minute when substitute Jon Obika unleashed an effort on the turn that Camp had to save.