The final match was decided in the first half.
Casemiro sent in 1-0 in the 33rd minute of the match, and Manchester United's lead was a fact after a VAR review.
United then extended their lead a few minutes later, when Newcastle's Sven Botman was last on the ball after some fine work by Marcus Rashford.
Swedish national team star Alexander Isak was substituted for the second half, but Newcastle did not receive any reduction.
The League Cup victory means that Manchester United secured the club's first title since 2017 (Europa League and League Cup).