Khiara Keating looked at the sky and let out a scream of frustration.

The Manchester City goalkeeper had already been responsible for one of Manchester United’s first-half goals when her misplaced clearance gifted Ella Toone her hat-trick and the opposition the game nine seconds after half-time.

City had fought back from three goals down to go in at half-time with the score at 3-2, but Keating’s second big error put United in the ascendancy once more and this time they were not going to allow their opponents a route back in.

Keating won the Women’s Super League golden glove last season and is a young goalkeeper with a lot of potential. She was superb when City were beaten by Barcelona in December and ensured the score was not worse than the three goals they conceded to the European champions. But City manager Gareth Taylor’s decision to select Keating, who has shared duties with the more experienced Ayaka Yamashita, with hindsight, looks a poor one.

“She’s [Keating] feeling a bit sore, like all of us,” said Taylor who refused to comment on United’s loan bid for Chloe Kelly who sat out Sunday’s match. “We win, lose and draw together as a team. We never push the blame in any direction. We started in a horrible fashion in the second half which gave all the momentum back to United.”

On that fourth goal, he added: “The players in front of her didn’t do their job. We didn’t block. The two players for United were able to run through. One of them blocked Khiara, the other one goes and scores. The players need to do their job.”

This was United’s first away victory against City in the WSL and it could not have come at a better time, with the result moving them above their rivals into third.

If City’s title hopes were slim coming into this, their chances now look even less promising. They are nine points behind Chelsea, who thrashed West Ham United 5-0 yesterday.

Brazilian forward Kerolin is expected to sign in the coming days and German international Jule Brand could also be brought in before January’s transfer deadline. Lauren Hemp and Khadija Shaw are also expected to return from injury soon. But the damage may already be done. City now look to be in a battle to qualify for the Champions League, with United and Arsenal two points above them.

All four of United’s goals came from defensive errors, the majority because of City’s insistence on playing out from the back. The absence of captain Alex Greenwood meant a lack of organisation in defence. In truth, United could have been four or five-nil up in the first 30 minutes.

While Keating was not directly responsible for the first goal, it was her poor clearance that led to United regaining possession before Toone produced a neat finish from a tight angle. The second had a hint of offside but once again exposed City’s defensive frailties as they failed to clear a corner, leaving Leah Galton with a tap-in from close-range. At that point City manager Taylor left his seat in the stands to return to the dugout but it made little difference as Keating played a goal-kick straight to Galton, who teed up Toone for her second.

City did manage to fight their way back into the game with goals from Vivianne Miedema and new signing Rebecca Knaak. But a bizarre kick-off routine saw United go 4-2 up just nine seconds after the restart. Miedema played the ball back to Keating, who was a long way off her line, and her poor touch led to an even poorer clearance that hit Elisabeth Terland in the face. The ball fell for Toone, who had an empty net to finish into.

“I was letting the girls know that I have never scored in a Manchester derby, never scored against City, as someone who supports Manchester United I know what these derbies mean,” said Toone. “I want to come into every game to make something happen on the pitch but today I wanted a goal, and I got three, so it was a special day for me. I could not have done it without the players.”