The Shrimps will get a chance for revenge over a Newcastle side that beat them in the same competition a few years ago with the only disappointment being that no fans will be present for the game next week.
In a tight game between two teams who both looked to play decent football, it was a goal from Aaron Wildig that separated the sides.
The midfielder, making his first start of the season after missing the first two weeks through illness, scored the only goal of the game on 22 minutes.
Liam McAlinden provided the assist with a clever through ball for Wildig, who found space from midfield to run past his man and provide a cool finish to chip the ball over the advancing Ian Lawlor.
The Shrimps started the game on the front foot with Carlos Mendes-Gomes seeing a shot blocked by Carl Piergianni, Alex Kenyon heading over a corner from Wildig and Jordan Slew drilling a shot over from the edge of the box.
Oldham looked a threat on the counter attack and forged a great chance of their own when Andrew Badan forced his way into the box, only to stab his final effort wide of the target when he should have done better.
Zak Dearnley then saw a shot blocked by Sam Lavelle and an effort from Conor McAleny struck Ryan Cooney before Morecambe went close to a second on 41 minutes when Cooney’s long-range effort dipped inches over the bar.
The second half saw chances at a premium with Morecambe having the better of the early stages after the break.
McAlinden went close to scoring his opening goal for the club with a shot on the turn that went just wide, while Adam Phillips fired inches off target moments after coming off the bench.
Oldham finally began to threaten in the closing stages and almost equalised at the death when Piergianni headed a left-wing corner just over the bar.
The visitors, who brought on former AFC Fylde striker Danny Rowe, laid siege to the home goal at the death but the Shrimps held on and produced some fine blocks to seal victory.
Morecambe: Halstead, Cooney, Lavelle, Davis, Hendrie, Wildig (Phillips 65), Kenyon (Diagouraga 65), O’Sullivan, Mendes-Gomes (Pringle 65), Slew, McAlinden. Subs not used: Turner, Mellor, Knight-Percival, Price.
Oldham Athletic: Lawlor, Jombati, Hamer, Piergianni, Borthwick-Jackson, Garrity (Rowe 83), Whelan, McAleny, Fage (Grant 65) Dearnley, Badan (Keillorr-Dunn 65). Subs not used: Woods, Barnett, Da Silva, Hough.
Referee: Ben Toner.