Wes Burns gave the Blues the lead on eight but Davis Keillor-Dunn equalised for Oldham four minutes before the break to leave the scoreline 1-1 at half-time at Portman Road in the first round of the FA Cup.
Town boss Paul Cook made one change from the team which won 4-1 at Wycombe on Tuesday with Cameron Burgess, a one-time Oldham loanee, replacing Hayden Coulson, who picked up a knock at Adams Park, at left-back as he did from the bench against the Chairboys.
Janoi Donacien was back among the subs after missing the last two matches having been ill.
After the players had taken a knee - with usual the exception of Toto Nsiala, who raised a fist - to applause from the Portman Road crowd, the Blues were first to threaten in the fourth minute.
Kyle Edwards took the ball to the byline on the left before crossing to Macauley Bonne, who headed at visiting keeper Jayson Leutwiler, who saved. Kane Vincent-Young hit the rebound wide from a tight angle.
But it took only another four minutes for the Blues to go in front. Bersant Celina fed Bonne down the left just inside the area, the striker cut inside and hit a shot which Wes Burns turned home from the edge of the six-yard box for his second goal in two games and his fourth of the season.
Town continued to dominate against the League Two strugglers and on 13 Lee Evans sent over a corner from the right which Bonne headed goalwards and keeper Leutwiler uncomfortably palmed wide.
Two minutes later, Evans cut a free-kick on the right back to Burns, whose shot was blocked.
Oldham presented no threat until the 27th minute when Dylan Fage crossed from the right and Hallam Hope looped a header which Christian Walton watched bounce well wide.
Three minutes later, Celina struck a powerful effort from just outside the box which Leutwiler batted away and referee Neil Hair bizarrely felt had gone out off Burns.
Blues skipper Morsy was booked for a foul in the 34th minute before Oldham created their first opportunity of the match.
Benny Couto crossed from deep on the right and Latics skipper Carl Piergianni’s header flew wide with the aid of a deflection.
Oldham were coming more into the game on and 38 Dylan Bahamboula, whose brother Plaisir had a trial with Town in the summer of 2012, hit a low shot beyond Walton’s far post.
In the 40th minute, Vincent-Young was just prevented from adding the final touch to an Edwards cross from the left, then from the corner George Edmundson, facing his old club, looped a header well over.
Having had a very comfortable afternoon, the Blues’ intensity had dropped somewhat and in the 41st minute the visitors levelled.
Nsiala failed to properly deal with a ball down the middle and Keillor-Dunn took it on a couple of paces before curling a shot beyond Walton’s left hand from the edge of the area.
Moments before the whistle, Keillor-Dunn played a ball to the right of the box towards Jordan Clarke but Edwards took it away from him as he was about to shoot.
Town had once again been guilty of allowing a side back into a game in which they had been ahead and very comfortable.
After gaining their early advantage, the Blues were well on top, although without creating too many chances to add to the lead.
However, they became more casual as the half wore on and the Latics had had a couple of opportunities prior to Keillor-Dunn’s goal.
Until then, Oldham had shown little and if Town play with their earlier intensity then they should have little trouble in confirming their place in round two.
Town: Walton, Vincent-Young, Nsiala, Edmundson, Burgess, Morsy (c), Evans, Burns, Celina, Edwards, Bonne. Subs: Hladky, Donacien, Penney, El Mizouni, Harper, Aluko, Chaplin, Fraser, Pigott.
Oldham: Leutwiler, Clarke, McGahey, Piergianni (c), Whelan, Hope, Keillor-Dunn, Fage, Bowden, Bahamboula, Couto. Subs: Adams, Dearnley, Diarra, Da Silva, Diarra, Vaughan, Modi, Southerington. Referee: Neil Hair (Cambridgeshire).