In an open and feisty first 45 minutes, Oldham came closest to scoring when midfielder Chris Taylor was not closed down and he let a shot fly from 40 yards that thudded off the post with Notts keeper Stuart Nelson well beaten.
County's best chances saw a brilliant cross from Alan Judge met by the powerful head of Daniel Bogdanovic, before Sheehan fired in a long-range effort, but both were saved by Dean Bouzanis.
The second half lacked the thrust of the first, but Notts should have taken the lead when Judge swung a deep ball to the far post, where an unmarked Lee Hughes could only head straight at Bouzanis.
But in the final minute of normal time, Lloyd Sam tricked his way into the area before laying the ball off for Sheehan to slam home from the edge of the area.
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