Goals from Ryan Williams and Tony Diagne sealed the points for the Shrimps, who climbed up to fourth place in League Two, and piled more pressure on under-fire Bury boss Kevin Blackwell and his struggling side.
Tom Soares went close early on, his deflected shot rebounding off a post, while Padraig Amond was denied at the opposite end by Brian Jensen.
Andy Procter got into some good positions for Bury, side-footing wide on one occasion and seeing Barry Roche tip a goalbound header over the bar.
The Shakers enjoyed another good chance early in the second half but Roche was equal to a powerful shot from Anton Forrester.
Having created little of note, Morecambe took the lead in stunning fashion when Williams curled home a superb free-kick from 30 yards, Jensen unable to keep it out despite getting a hand to it.
Procter nodded inches wide of a post from a Shaun Beeley cross but Morecambe wrapped up victory in injury time when Diagne rifled home from a tight angle, extending the club's unbeaten run to eight games.