The minnows form the Midland Alliance were playing their 10th cup tie of the season and put on a brave show but they rarely threatened to pull off one of the biggest ever shocks.
Chasetown were roared on by almost 2,500 fans even though they often play in front of just double figure crowds in the league.
The amazing turnout showed what an achievement it had been to reach the first round proper and Chasetown's players relished the big night by staying on the pitch for several minutes after the final whistle.
They performed well for the first half hour, creating the best chance when Karl Edwards headed beyond the far post.
But Oldham went in front on 31 minutes as Paul Warne hit an unstoppable drive from 20 yards which flew in off the crossbar.
Chasetown's opportunity to draw level came just before half time when Kevin Thompson's header had to be kicked out by Oldham keeper Chris Day.
The Latics doubled their lead on 56 minutes as Chris Porter tapped in from six yards following a cross by the lively Andy Liddell.
Liddell almost scored himself but his long-range shot was saved by Simon Bryan the Chasetown keeper.
Bryan was beaten again in the 75th minute when Porter blasted his second goal of the night with a stunning 25-yard drive which flew inside the post.
Paul Edwards hit the post for Oldham before they wrapped up victory on 84 minutes through substitute Chris Hall who converted an eight-yard header from an Edwards cross.