Danny Rose flicked a header home in the seventh minute for the only goal of the game.
Keith Hill named one change to his starting eleven from last week’s victory over Port Vale, with Donal McDermott coming in for Joe Bunney.
There was a great atmosphere inside Spotland and this transferred onto the pitch for what was a frenetic opening five minutes. Dale started well but it was the visitors who took the lead from a corner kick.
Chris Hussey’s delivery was met by Rose who flicked a near post header over Joel Castro Pereira and into the far corner.
An early blow for Dale which would require a positive response, and only a good stop from Daniel Bachmann denied an equaliser. Good football from Dale saw James Hooper played in one-on-one, but the Bury stopper saved well with his body.
Castro Pereira was called into action shortly after at the other end to deny Leon Clarke. The Bury striker looked to control with his arm, but as he looked certain to score the on-loan Dale goalkeeper rushed out quickly to save at his feet.
It was a crucial stop to keep Dale within arm’s reach, and the rest of the half belong to Keith Hill’s men as they built up a head of steam.
Donal McDermott found himself behind the Bury defence, but after cutting in on his left foot he sent his shot wide.
The Irishman had an effort deflected out for a corner, as did Hooper as Dale were getting closer.
There were a number of melees inside the Bury area but the ball just wouldn’t fall in favour of Dale. Ian Henderson could only chip over from close range as he was being forced away from goal, before he had an effort well saved after jinking past a couple of Bury defenders.
Half-time was unwelcome for Dale who finished the half strongly, but the first chance of the second period fell the way of Dale, with John O’Sullivan’s effort from distance flying narrowly over the crossbar.
It would be his last act, as he and McDermott were replaced by Peter Vincenti and Andy Cannon with a little over ten minutes played after the break.
Calvin Andrew had a header easily saved by Bachmann, whilst good defending prevented Hooper troubling the Bury goal after a great run from Henderson.
Michael Rose replaced Rhys Bennett as Keith Hill used his final substitution, fellow substitute Cannon moved to right back.
Neither side were creating much in front of goal as Dale tried to force their way forward and grab a late equaliser.
As the game entered four minutes of added time Jim McNulty had an effort which he sent over the bar after showing good feet inside the area.
That would be the last action of the game as Bury held out for the victory, knocking Dale out of the FA Cup at the second round stage.
It is back to league action next weekend for Dale, as Keith Hill’s men travel to Swindon Town.
Dale: Pereira, Bennett, Lancashire, McNulty, Tanser, Camps, O’Sullivan, Hooper, McDermott, Andrew, Henderson.
Subs: Lillis, Eastham, Vincenti, Alessandra, Rose, Cannon, Bunney.
Bury: Bachmann, Hussey, Clarke, Etuhu, Clarke, Mayor, Jones, Soares, Cameron, Rose, Dodoo.
Subs: Lainton, Pugh, Pope, Nardiello, Eagles, Burgess, Brown.