The Newcastle goalkeeper had recorded a shut-out in the Young Lions' opening game, a 3-0 win against Argentina, before being rested for the 1-1 draw with Guinea.
But England - coached by former Magpies number two Paul Simpson - knew that a draw against hosts Korea would be enough to see them qualify for the knockout stages.
And Kieran Dowell's second-half strike saw them top Group A, with Woodman helping England to protect their lead.
Adam Armstrong - who had started England's previous two games and scored against Argentina - was an unused substitute.
England will now play their last-16 tie on Wednesday.