Rudd struck with an 89th-minute overhead kick to give the fifth-placed Rebels a victory which ensures they stay tucked in behind neighbours Curzon Ashton, 2-1 winners over Lancaster.
But it was a win achieved at a price for Karl Marginson's men, who lost leading scorer Rory Patterson with a knee injury.
Pat McGuire had given lowly Woodley a 47th-minute lead before Jamie Baguley equalised midway in the second half.
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Free Red, Manchester (25/03/2008 at 11:05)
Tony Nuttall, Barnsley (25/03/2008 at 21:02)