He was handed a surprise start for the Cottagers before being replaced by Darren Bent with 14 minutes to go.
On handing the 19-year-old striker his debut, new Fulham boss Felix Magath said: “I see no gamble in it because he is a very talented player and I was satisfied with him. He did a lot of work for the team.”
Woodrow made his Luton debut at 16 years 12 days and was capped at England U17 level before joining Fulham for a six-figure fee that could exceed £1million, where he is contracted until 2016.
Earlier this season he scored four times in 21 appearances while on loan at League Two Southend United.