Jonathan Forte grabbed a double on his debut but Latics had to settle for a point in the opening game of the season.
U's captain Magnus Okuonghae had given the home side the lead early in the game but Forte's double gave Latics the advantage going into the break.
Midfielder George Moncur equalised for Colchester just before the hour mark but neither side could get the decisive winner and both had to settle for a opening day draw.
Latics made the worst possible start, falling behind within the first seven minutes of the game. Magnus Okuonghae pounced on a loose ball in the penalty area and made no mistake from six yards to put the U's ahead.
The goal really kicked the visitors into action as they enjoyed more of the possession and started to dictate proceedings.
Their dominance paid off on 18 minutes as Forte got them back on level terms through a superb individual finish. The winger picked up the ball on the left-hand side and ghosted past the Colchester defence, rounding Sam Walker and he knocked the ball into an empty goal.
The visitors continued to press their opponents and went close again five minutes later. James Dayton's cross found the head of Jonson Clarke-Harris but the striker could not keep his effort down.
Colchester were forced into making a change on the half hour mark as Moncur replaced Craig Eastmond and minutes later, the U's should have been ahead.
Jabo Ibehre escaped the offside trap and lifted the ball over the head of Paul Rachubka but the ball fell inches wide of the goal.
Latics capitalised on that missed chance and took the lead on 40 minutes through a second goal from Forte. Clarke-Harris found Brian Wilson in acres of space and his cross was finished by the forward to score his second goal of the game.
Colchester started the second half on the front foot and won a free kick on the 18-yard box but Freddie Sears' free kick smashed against the wall and the chance was cleared.
The home side did finsd an equaliser on 58 minutes through substitute Moncur. Genseric Kusunga was dispossessed in the middle of the field by Sears and the striker let rip from 25 yards out, which rebounded off the post and was finished by the West Ham loanee.
With pressure building, Clarke-Harris was forced into defensive duties as he had to clear off the line from a corner.
Latics were finding chances hard to come by but Clarke-Harris found space in the centre with 15 minutes to go but fired his shot into the side-netting.
William Gros and George Elokobi were introcued into the game for their debutes and the latter recieved a round of applause from both sets of supporters.
Both sides looked dangerous going forward but clear-cut chances were hard to come by.
The referee called time on the game with Latics picking up their first point of the season.
Colchester United: Walker, Gordon, Okuonghae, Eastmond, Gilbey, Ibehre, Sears, Wright (Vose 64'), Eastman (Moncur 31'), Clohessy, Massey (Holman 84').
Subs not used: Lewington, Thompson, Bean, Szmodics.
Oldham Athletic: Rachubka, B.Wilson, J.Wilson, Kusunga, Mills, Winchester (Philliskirk 85'), Jones, Kelly, Dayton (Elokobi 80'), Forte (Gros 80'), Clarke-Harris.
Subs not used: Coleman, Brown, Dieng, Mellor.
Goals: Colchester United (Okuonghae 7', Moncur 58') 2-2 Oldham Athletic (Forte 18', 40')
Attendance: 4,023 (623 visiting supporters)