Morecambe might even have snatched an away win after soaking up plenty of pressure, but Carlton drilled his first opportunity straight at goalkeeper Shwan Jalal and three minutes later his header clipped the top of the bar when he was left unmarked.
Bournemouth had chances in the first half to have gone ahead, but the nearest they came to scoring was when a right-foot shot from on-loan striker Michael Symes struck the post.
Darren Anderton had a shot blocked at close range, and Warren Cummings had an in-swinging corner cleared from the line.
Bournemouth struggled to make an impact in the second half, but a shot from Danny Hollands drifted wide from the edge of the area as Morecambe held on to go five matches unbeaten.
Jimmy Quinn's Bournemouth have still not wiped out the 17-point deficit imposed on them by the league for going into administration and need one more point to reach zero. The Cherries remain second from bottom of the League Two table.