Ryan Kidd's side were going into the game at SportsDirect.com Park hoping to improve on last season's FA Youth Cup campaign, which saw them knocked out in the first-round, ironically to last night's opponents.
This time the lads didn't disappoint, progressing to the next round after a well-deserved win and all-around dominant performance.
The Shakers held a 2-0 lead at half-time as Callum Hulme's free-kick was swiftly followed by Cameron Hill's piledriver and it was Rob Harker who sealed the deal with his volley in the 51st minute.
The first chance of the game fell to the home side in the 4th minute, when a corner was floated into the crowded Bury box by Chinedu Uche, but fortunately for the Shakers, it was headed wide by Tom Hamer.
Oldham tried to make a break on goal in the 14th minute with Max Norman skipping up the wing, but he was met by Bury captain Ryan Cooney on the edge of the box, who read the situation well and managed to calmly clear the ball to safety.
A minute later Bury had the ball in the back of the net but the referee’s whistle had already blown for a foul on goalkeeper Joe Boyling.
Shortly after, the Shakers were awarded a free-kick in a very dangerous position on the edge of Oldham's box. Both Callum Styles and Rob Harker hovered over the ball, but it was Harker who stepped up. The ball was hit with real force, but unfortunately with just a bit too much, which saw it fly over the bar.
On the 24th minute, Javid Swarby-Neavin was booked for a late challenge which gave Bury a second free- kick in another dangerous position. This time it was Callum Hulme who fancied his chances and he didn't disappoint, as he curled the free-kick into the top corner.
It took only two minutes for the Shakers to double their lead with a cracking 25-yard effort from Cameron Hill. Hill drove forward finding the space to unleash a shot and fired it straight past a helpless Boyling into the bottom corner.
There was a change for Oldham at the break as Festus Arthur replaced Declan Baldwin.
It was the Latics who had the first chance of the second half. Max Norman raced toward the Bury goal, he found the space and pulled the trigger releasing a decent effort, but Moloney managed to get his palms to the ball to push it behind for a corner.
On the 51st minute, the Shakers were back into their stride and Rob Harker grabbed the Shakers' third goal of the night. The young striker found himself on the end of a great corner from Callum Styles inside the crowded box. He somehow found the space to unleash a powerful volley which fired past Boyling into the back of the net.
Oldham's best chance of the half came close to the hour mark when Chinedu Uche found himself unmarked on the edge of the box after a tidy bit of play from the Latics. He looked almost certain to score, but his strike had too much behind it sending it over the crossbar.
Oldham's Sheridan nearly managed to pull a goal back with just five minutes of the game remaining as he met substitute Bailey Whalley's cross into the box but his sweetly-struck volley forced a good save from Moloney.
It was a slightly quieter second-half for both sides, but it was Bury who kept control with an overall dominant attacking and defensive performance, to see them come away with a triumphant 3-0 victory against last season's successors and a place through to the next round to play Wigan.
Oldham Athletic: Boyling, Swarby-Neavin (Norris 77'), Hamer, Lent, Sheridan, Antoine, Uche, Baldwin (Arthur 46'), Dry, Scholes-Beard, Norman (Whalley 70').
Subs not used: McFarlane, Amankwaa
Bury: Moloney, Nyaupembe, Hatto, Styles, Shotton, Cooney, Adams (Skinner 88'), Hill, Harker (Williams 82'), Hulme, Da Silva (Lockett 65').
Subs not used: Ondua, Williams
Goals: Oldham Athletic 0 – 3 Bury (Hulme 25', Hill 27', Harker 51')