Scotland star Scott McTominay stepped off the bench to ensure Manchester United did the double over rivals Manchester City.
The midfielder struck the second late on after a mistake from Ederson, who will be criticised for his part in both Manchester United goals.
The Manchester City goalkeeper allowed Anthony Martial's shot in the first half to slip underneath him before throwing the ball straight to McTominay to score from 30 yards.
Pep Guardiola was left baffled by Ederson's mistakes as United claimed their first league double over City since 2009/10.
City were without playmaker Kevin De Bruyne for their derby against rivals Manchester United at Old Trafford.
With the second leg of their Champions League tie against Real Madrid coming up next week, City decided not to risk the Belgian, who landed awkwardly on his shoulder in the Carabao Cup final last Sunday.
De Bruyne did not even make the bench but Wembley man of the match Phil Foden was handed a starting place. Ederson returned in goal and Joao Cancelo was preferred to Kyle Walker at right-back.
United made seven changes from Thursday's FA Cup win against Derby.
Harry Maguire recovered from an ankle injury to skipper the side at Old Trafford, where Aaron Wan-Bissaka and Daniel James also overcame knocks to start.
United took the lead with half an hour gone as Anthony Martial volleyed in from a free-kick.
Bruno Fernandes chipped a ball over the wall and Martial ran on before hitting a shot that Ederson allowed to go under his hand as he dived to his right.
They then should have had a penalty when Fred was chopped down but the Brazilian was booked for diving and VAR decided against overruling referee Mike Dean.
United sealed the victory following another mistake by Ederson in stoppage time.
The City keeper attempted to feed Benjamin Mendy with a throw which saw the ball intercepted by McTominay and he curled into the empty net with Ederson well off his line.
