The home team Liverpool took the lead already in the third minute when Mohamed Salah received the ball in the penalty area, turned nicely and pounded the ball up.
With 20 minutes played, the visitors could have scored the tying goal after Sean Longstaff came through the middle, but his kick went wide.
Already in the starting eleven, it was noticed that Liverpool really went for victory.
The whole quartet was lined up with Salah, Roberto Firmino, Sadio Mane and Diogo Jota.
They had several chances to extend the lead, but at the break the score was 1-0.
The reigning champion looked to be heading for victory, but it was a dramatic extra time.
Newcastle first had the ball in goal once, but then Callum Wilson's goal was rejected after scrutiny.
The return from Alisson took Wilson's hand.
Instead, the receipt goal came during the overtime period.
19-year-old Joe Willock got the ball in the penalty area and via a control it went in behind the goalkeeper.
With the cross, Liverpool, who have had a tough time in the league since New Year, are sixth in the Premier League and it looks tough in the battle for places in next season's Champions League.
The top four get to play CL.