The midfielder curled the ball over the wall in the first half to give Latics the lead and they held on to put Latics into the hat for Monday's draw.
The FA Cup tie started at pedestrian pace with Latics bossing the possession but struggled to create clear cut chances.
Leyton Orient's Josh Wright had the first chance of the game on 10 minutes but his shot from the edge of the box was well handled by Paul Rachubka.
Latics were dictating proceedings with midfielders Liam Kelly, Mike Jones and Carl Winchester linking well as they looked to create an opening for the strikers.
Midway through the first half, Jones felt O's defender Scott Cuthbert had handled in the area
Dominic Poleon, on his first start since Chesterfield last month, was causing a nuisance in attack and almost presented himself with a chance on the half hour mark but his shot was deflected over the bar as he wriggled away from three defenders.
Jones and Winchester swapped wings just after the half hour mark and it played to Latics' advantage.
On 38 minutes, Latics took the lead. Kelly was fouled on the edge of the box and Jones got the free kick up and over the wall, leaving the goalkeeper rooted to put Latics ahead in the FA Cup tie.
A minute into added on time in the first half Danny Philliskirk was booked for diving and two minutes into the second half, Liam Kelly also received a yellow card.
Latics started the half on the front foot with Jones at the fore-front of the attack.
The midfielder robbed Cuthbert ten minutes into the second half and drove at goal but did not trouble Gary Woods in the Orient goal.
The O's came back into the game and were putting pressure on the Athletic back line but Genserix Kusunga and James Wilson did well to marshall away the strikers.
Latics were living dangerously and 20 minutes from time, Kusunga had to be alive in his own penalty area as former loanee Nathan Clarke headed across goal but the defender cleared off the line.
Two minutes later, the O's had the ball in the goal but the referee spotted a foul in the box and it prevented Orient from drawing level.
The home side had to defend resolutely going into the final ten minutes of the game.
Orient threw everything forward in a bid to get a replay from the game but Rachubka denied Cox from 25 yards five minutes from time in their best chance.
Latics hit the O's on the break deep into stoppage time and were unfortunate not to extend their lead.
Philliskirk received the ball and shot from 25 yards but it cannoned off the outside of the post and the danger was cleared.
The referee blew time on the game and it was Latics that progress through to the second round of the competition!
Oldham Athletic: Rachubka, B.Wilson, J.Wilson, Kusunga, Mills, Kelly, Jones, Winchester, Forte, Philliskirk, Poleon (Dayton 74').
Subs not used: Etheridge, Dieng, Lockwood, Mellor, Truelove, Tuohy.
Leyton Orient: Woods, Cuthbert, Baudry (Sawyer 83'), Cox, Lowry, Batt (Bartley 58'), Clarke, Wright, Pritchard, Dagnell, Simpson.
Subs not used: Omozusi, Lee, Kashket, Adeboyejo, Legzdins.
Goals: Oldham Athletic (Jones 38') 1-0 Leyton Orient
Attendance: 3,034 (129 visiting supporters)