Oldham earned an FA Cup third round trip to Liverpool on 7 January after Chris Taylor's second-half strike proved enough to beat Southend.
Neil Harris and Bilel Mohsni forced fingertip saves from Latics goalkeeper Alex Cisak inside the first 18 minutes.
But Southend were down to 10 men on 38 minutes when Mohsni was sent off for fouls on Kieran Lee and Dean Furman.
James Wesolowski's lay-off then set up Taylor to smash home from 10 yards for the only goal just before the hour.
Oldham's trip to Anfield, where they have not won since 1913, will be their first meeting with Liverpool in 17 years - since their Premiership days.
Oldham manager Paul Dickov told BBC Radio Manchester:
"I'm very proud for lots of reasons. For my staff, for my chairman, for the directors, for the players and everyone who works at the football club.
"For us, at the start of the season, to get to the third round and hopefully draw a Premier League club was like our cup final.
"It's fitting that someone who supports the club, somebody who loves the place, scored the goal that gets us there."
Southend United manager Paul Sturrock told BBC Essex:
"I've let everybody down. I know there's a footballer in there [Bilel Mohsni], but too many times he's let us down.
"It's cost us a lot of money. I pick the team and I made a decision to play him and it's shot us in the foot.
"I should have probably taken him off. He just looked as if he was a walking foul again."