Manchester City were the leading team in the final, but it took a long time before they got a hole in Tottenham.
The goal came first in the 82nd minute when star Kevin de Bruyne's free kick reached Aymeric Laporte's head.
The league title means that Manchester City can still win a triple this season.
They have virtually secured the Premier League victory and are also in the semi-finals of the Champions League.
In the CL, they meet Paris Saint-Germain in a double meeting.
With the title, Man City touches the number of league cup victories in a row.
Liverpool also won four straight between 1981 and 1984.
A change of coach from José Mourinho to former player Ryan Mason, 29, did not help Tottenham, who have not won a title since the 2008 League Cup.