Oldham failed to take their chances as Carlisle held on to secure a point.
Lee Hughes had three good chances to score in the first half but fired over from the edge of the box and had two good efforts saved by keeper Tim Krul.
Hughes missed another good opportunity in the second half while team-mate Mark Allott blasted way over the bar.
Carlisle substitute Scott Dobie headed just over and Cleveland Taylor lifted a shot over the bar as the visitors almost snatched all three points.
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