The visitors were poor until they fell behind to Reuben Hazell's goal for Oldham, but they fought back for a well-deserved share of the spoils.
Both sides went into the game low on form as Crewe were without a victory in six attempts and Oldham's winless run stretched back eight matches - a sequence which cost them any chance of securing a play-off spot.
But relegation battlers Crewe finished happier with a point and might even have snatched all three after Moore's 89th-minute leveller.
In an archetypal game of two halves, Hazell was the first to go close when he hooked marginally over the bar from a set-piece.
Crewe midfield man Gylfi Sigurdsson was unlucky to miss the target with a powerful drive, but Oldham were in charge and threatened again as Chris Taylor let fly from 16 yards.
Crewe keeper John Ruddy denied Danny Whitaker before bright Oldham approach play led to Deane Smalley flicking a shot just wide.
The visitors, however, displayed their threat on the half-hour mark after Calvin Zola set up Clayton Donaldson, whose attempted lob cleared the bar.
Crewe were made to pay four minutes before half-time as Oldham - much the better side in open play - broke through with Hazell's third goal of the season.
Left-back Hazell appeared at the far post and, having been found by Smalley's cross from the right, he guided his six-yard header across the helpless John Ruddy.
Oldham keeper Greg Fleming saved from John Brayford and Crewe nearly equalised on the stroke of half-time when Zola's effort was bundled off the line, but they had an escape as Steven Kabba almost deflected in Julien Baudet's clearance.
Alex were guilty of a dreadful error when Billy Jones sent in a free-kick to Zola, who somehow missed the target from only four yards.
Yet Crewe started gaining the upper-hand and they were denied what looked a clear penalty for Hazell's challenge on substitute Shaun Miller.
Their enterprise was finally rewarded after weak Oldham defending allowed the ball to reach Moore, who produced a calm finish inside the far post from 12 yards.