The visitors belied their position at the bottom of the Unibond Division One North, as they got another good result against the Rebel Reds.
Only a win was good enough to give FC a chance of going up without the need of the play-offs but they could not break down the visitors in the first half.
When Jamie Kay put Woodley ahead with a speculative effort from the touchline, United were staring a shock defeat in the face.
They had to wait until injury time for the equaliser to come, Jerome Wright firing a left-footed shot into the top corner.
FC must now aim to go up via the play-offs.
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