The midfielder, aged 17 years and 45 days, has broken the record previously held by Michael Owen, who was 17 years and 145 days when he scored his first goal in 1997.
The Welsh teenager made his senior debut for the Reds just four days before, coming on in stoppage time for Georginio Wijnaldum in the 2-0 victory over Sunderland.
However, his second appearance for the club was even more memorable, as he came off the bench to net his first goal for the club.
With the game tied scoreless, Woodburn was sent on with 23 minutes remaining against Leeds, netting the second goal in a 2-0 victory to help Jurgen Klopp's side reach the EFL Cup semi-final.
An academy graduate, he has been with Liverpool since 2010, working his way up through the ranks at Anfield before being included in Klopp's senior squad.
"I think Ben is mentally ready to start a game," Klopp told the club's official website after handing him his debut.
"At that moment I thought it was a good idea [for him to play against Sunderland], he deserved it and I thought: 'Come on, let's go.' It was only a few minutes. He was ready for it.
"It was only after the game that I remembered it's now really difficult to keep him back again, not for Ben or for me, but for the public.
"We've shown him the Premier League for the first time, but the best news for him is there is so much time for him to improve and develop. We will help him."