A goal from Anton Robinson saw the Shrimps suffer another away defeat.
Robinson volleyed past Barry Roche from 12 yards out after the Shrimps failed to deal with a Danny Hollands's throw-in. Brett Pittman headed down and Robinson's strike gave Roche no chance.
The goal came as the home side dominated the eatly stages with Alan Connell heading wide and Lee Bradbury failing to test Roche.
The Shrimps took a long time to get going and failed to test former keeper Shwan Jalal with Phil Jevons both volleying well over.
The second half began with Mullin diverting an excellent Garry Hunter right wing cross inches wide of the target at full stretch. Mullin had a second golden chance on 83 minutes but missed the tgarget from close range when he should have tested Jalal.
The home side went close themselves on a couple of occasions with Brett Pitman heading just wide and Josh McQuoid denied by a superb Roche save.
Sammy McIlroy went for the same side that beat Port Vale 1-0 at Christie Park last week.
Bournemouth: Jalal; Bradbury, Cummings, Garry, Wiggans; Bartley; Connell, Robinson, Hollands; Fletcher, Pitman. Subs:Thomas, Cummings, Igoe, Goulding.
Morecambe: Roche; Moss, Bentley, Haining, Parrish; Stanley, Panther, Hunter, Duffy; Jevons, Mullin. Subs: Davies, Artell, McLachlan, Drummond, Curtis, Wainwright, Jackson.
Ref: S Tanner.
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