Apparently this is a commonmisapprehension and the nearest valid answer is outlined in the link below from the FA website
www.thefa.comTheFA/WhoWeAre/ContactUs/.../trivia
Aston Villa won the cup fianl one nil and a player called NEVER scored the goal.fact and true.can't remember year
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noone can win a match without scoring a goal if its level at the end of regulation than they go on to extra time after that its penalty kicks after two rounds if its still level it will be sudden death penalties
man utd won the fa cup without scoreing
it was a Steve Watson own goal vs everton