The Fulham youngster found the net inside three minutes but some poor defending means England must now draw with Colombia to qualify from the group stage
Woodrow gave England the lead in the third minute, but a poor showing from Gareth Southgate's men eventually ended in Lee Changmin firing in a second-half equaliser.
Woodrow was twice denied a winner in the closing stages, and the Three Lions must now avoid defeat against Colombia on Friday to make sure of a place in the third-placed play-off.
Southgate rang the changes for the second match in succession as captain Jack Butland and Liam Moore paid the price for their mistakes in the defeat to Brazil while Woodrow started for the first time in the tournament.
And it was the Fulham man who was quickly into the action as Brad Smith fed Jake Forster-Caskey, and he in turn found Woodrow, who had time to poke past goalkeeper Kim Dong Jun with a first-time finish.
The 19-year-old really should have had a second moments later as he was fed by Nathaniel Chalobah from midfield, but his shot proved weak and Kim was able to hold on low to his right.
From there the game settled down somewhat, with Lee Kwang Jong's side able to control possession for much of the first half without really threatening.
Bayer Leverkusen's Ryu Seung Woo twice went close as 35-yard effort had Jonathan Bond scrambling as it flew just over the crossbar before he fired straight at the Watford goalkeeper from the edge of the box.
England lacked any real penetration towards the end of the half, and they almost conceded straight away at the start of the second as Ahn Hyunbeom cut inside and forced Bond into a fantastic save via a Michael Keane deflection.
At the other end substitute Solly March tested Kim with an effort from 25 yards, but after the goalkeeper parried, the Asian outfit went up the other end and grabbed an equaliser.
Lee picked up the ball in midfield before running unchallenged at the heart of the England and firing an effort into the bottom corner from 20 yards with Bond motionless.
That seemed to kick the Three Lions into life, and captain James Ward-Prowse struck a shot straight at Kim.
At the other end goalscorer Kim sent an overhead kick narrowly wide while Nathan Redmond tested Kim with a fierce effort from 20 yards as he began to have an influence from the left.
England thought they had won it twice in the final seconds as first Woodrow had a header ruled out for offside before Kim pulled off a miraculous stop to deny the Fulham man after Luke Garbutt's cross from the right.