Robinson grabbed the only goal of Saturday's League Two clash at Dean Court in the 18th minute, firing a rasping right-footed shot past Shrimps goalkeeper Barry Roche after Steve Fletcher had flicked on Lee Bradbury's long throw.
The second-placed Cherries thoroughly deserved their win against an out-of-sorts Morecambe, who only managed one meaningful shot on target.
The lively Josh McQuoid wasted a great chance to double Bournemouth's lead before half-time when he burst through but shot across the face of goal with only the keeper to beat.
Bournemouth called the tune for the bulk of a scrappy second half, but were unable to turn their pressure into goals. Roche tipped a fierce shot from McQuoid over the bar and saved again from a hooked shot by Pitman.
Morecambe, who had beaten Bournemouth 5-0 before Christmas, stepped up the pressure in the closing stages, with Paul Mullen hitting the outside of the upright.