Lewis Baker bags winner to hand Dermot Drummy's side Premier League title.
The midfield master seized his opportunity in the 79th minute, capitalising on loose United defensive play to cut across the edge of the area and curl an immaculate shot past Ben Amos.
It was the third of three wonderful goals in a final that lived up to pre-match expectations and left a 13,000-strong crowd richly entertained.
United, the defending champions, had taken an early lead when Tom Lawrence, who bore more than a slight resemblance to Ryan Giggs as he tore down the wing in his No 11 shirt, bent in a well-taken goal.
Giggs, watching on in the stands after a busy day in which he had met prospective new manager Louis van Gaal in Holland, would have been impressed by the young winger's composure when James Wilson teed him up following Saidy Janko's low cross.
Chelsea equalised 10 minutes later when Belgian whizzkid Charly Musonda drove at the United defence, left three red-shirted defenders trailing and fired a low shot into the bottom corner.
The visitors were the superior team after that, showing the greater threat going forward and looking resolute at the back on the occasions when United troubled them.
The win caps a double for the London club's Academy after they beat Fulham to claim the FA Youth Cup last week.