United took the lead on Monday night through midfielder Nick Powell in the 34th minute but Liverpool hit back just before the break as Valdes was beaten by Jerome Sinclair to level the scores.
However, Paddy McNair???s second-half strike was enough to hand the home side victory over their rivals from Merseyside.
There was plenty of speculation throughout the day that Darren Fletcher could be set to make his final appearance for United but there was no place in the squad for the Scotland midfielder as he continues to be linked with a move to West Ham.
Despite the 30-year-old???s absence, Warren Joyce named a strong United line-up, including Valdes, Anderson and Powell.
It was the midfield duo who combined to produce the first opening of the game as Powell raced onto Anderson’s through ball, but the 20-year-old???s attempt flew juast wide of the post..
However, the former Leicester City midfielder was not to make the same mistake twice as he rose highest to head his side into the lead from Andreas Pereira’s free-kick.
Liverpool responded just before the half-time interval as Cameron Brannagan pounced on Reece James’ loose pass and found Sinclair in space before the striker beat Valdes easily at the near post.
The home side made a fast start to the second half as McNair roared forward, linking with Saidy Janko before the Swiss youngster flicked the ball back into the path of the defender, who powered home a strike with his right foot within two minutes of the restart.
Liverpool enjoyed plenty of possession as the game wore on but it was United who went closest to grabbing another goal through Pereira, Jesse Lingard and Anderson as they went on to secure victory.