The Rebels went into the clash with the Stockport side five points behind leaders Bradford Park Avenue knowing three points from their game in hand would take the race to Saturday's final day.
But a speculative 68th minute lob from way out on the left wing by Jamie Kay left FC United contemplating next Tuesday's play-off semi final tie.
Striker Jerome Wright grabbed a fine last-minute equaliser, but it just was not enough.
The point gives Woodley some much-needed breathing space in their battle, with Bridlington Town, to avoid relegation.
Woodley could have gone in front eight minutes before the break when striker Andy Farrell saw a close- range volley bravely blocked by home skipper Dave Chadwick.
They were forced onto the back foot again early in the second period, as FC United increased their intensity, but weathered the storm.
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Free Red, Manchester (24/04/2008 at 11:09)
The real result last night is that with Curzon losing away to NBS a point was all we needed to take second place in the league and if we win on Saturday away to Garforth Town we will have the home advantage in the play offs. Viva la revolution, come on FC.