The Latics saw Chris O'Grady hit the woodwork twice in the second-half, while Pawel Abbott also saw an effort come back off a post.
But Oldham were already in a commanding position thanks to Whitaker curling in an effort from 20 yards after 13 minutes.
Alessandra doubled their lead 10 minutes before the break and, despite making 10 changes at half-time, Oldham still controlled affairs after the interval, only to be frustrated by the woodwork.
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