Rene Howe gave Morecambe a 14th minute lead, although Paul Scott drew the Shakers level just five minutes later.
Bury then went in front through David Artell's own goal on the half-hour mark and the Shakers deservedly hung on to make it three wins from three and leave Morecambe with just a point so far.
Bury striker Andy Bishop returned in place of Glynn Hurst after missing last week's 3-1 win at Chesterfield, while Morecambe boss Sammy McIlroy made three changes following the 3-1 home defeat by Rotherham.
The visitors had the better of the opening stages, with Howe turning the ball past Wayne Brown after Neil Wainwright put a corner back into the Bury box.
Matt Blinkhorn was booked for a late challenge shortly after, with Bury winning a corner from the resulting free-kick.
And Shakers skipper Scott rose highest to head home from Brian Barry-Murphy's in-swinging delivery.
Morecambe replied with Blinkhorn heading wide from Howe's cross after Efe Sodje failed to deal with a long ball.
But the Shrimps found themselves behind on the half-hour mark after Elliott Bennett raced past Henry McStay on the right wing to square for Bishop.
Artell didn't know whether to block the cross or turn it wide for a corner and did neither, inadvertently turning the ball past his own keeper from six yards.
Again Morecambe responded positively and the recalled Wayne Curtis crept past Scott before flashing a shot across the face of goal.
Brown then did well to deny Howe at his near post 10 minutes after the restart, while Curtis volleyed wide from Blinkhorn's lay-off.
Bennett sent a long-range effort well wide before Barry Roche prevented sub Danny Racchi and Andy Bishop sealing it late on, but Bury had done enough.