Substitute Dean Smalley was the hero when he bundled home the equaliser in the 88th minute, just six minutes after coming on as a substitute.
Colchester keeper Dean Gerken only half punched away a free-kick delivered by Neal Eardley and when Lee Hughes slid the ball back into the danger zone, there was substitute Smalley to steer home from six yards out.
Oldham will feel that it was a point they deserved, especially as they fought back from 2-0 down and also hit the woodwork in the first half when Andy Liddell's long range shot hit the bar.
Colchester's star man, Mark Yeates netted both the U's goals both with great finishes.
Yeates broke the deadlock just before half-time when volleying superbly past keeper Mark Crossley and into the far corner of the net.
It meant that the Irishman will forever be remembered as scoring the first-ever goal at the U's new stadium.
Yeates doubled the lead in the 63rd minute when crashing home an unstoppable shot from the edge of the box.
At that point, it looked as though Colchester would cruise to victory, but they fatally conceded a goal within 60 seconds, when winger Chris Taylor latched on to a pass from Hughes and beat Gerken with a low drive from the tightest of angles.
The U's nearly restored their two-goal advantage when a header from Clive Platt from a cross by Yeates rattled the post.
It still looked as though the home side would hang on until Smalley struck with his late equaliser.
This result ended Oldham's 100 per cent record at the start of this season, but they will still be happy with a point.