The clubs' 151st league meeting was decided by a goal from Argentina's Sergio Aguero in the 63rd minute after United centre half Chris Smalling had been sent off in the first half for two yellow cards.
With Rafael Da Silva missing the game and Marcos Rojo forced off in the second half, a makeshift United defence comprising Antonio Valencia, Michael Carrick and teenagers Paddy McNair and Luke Shaw came under increasing pressure.
The surprise was that City were pushed back and suddenly looked edgy once they had scored.
In the end, City were pleased to hang on for a fourth successive league win over the neighbours -- the first time that has happened since 1970.
The other depressing historical note for Van Gaal was that he has now presided over United's worst start to a season since 1986, when Ron Atkinson was sacked and Alex Ferguson appointed.
The result left United in ninth place, with 13 points from 10 games and no away wins.
City meanwhile returned to within six points of leaders Chelsea, two behind second-placed Southampton.
Having lost Aleksandar Kolarov to injury in the warm-up -- Gael Clichy deputising -- City were slow to settle until midway through the first half when United's David De Gea had to make two fine saves in quick succession.
He thwarted Jesus Navas from barely six metres out and then saved from Aguero, both men needing treatment after their subsequent collision.
Smalling picked up his foolish first yellow card for raising his foot in attempting to block a clearance by City goalkeeper Joe Hart and seven minutes before halftime he clearly fouled James Milner and was dismissed.
United, who brought on Carrick for his first appearance of the season after a long injury, could have conceded two penalties in the last few minutes before the interval but referee Michael Oliver gave them the benefit of the doubt as City appealed for apparent fouls against Aguero by Marouane Fellaini and Yaya Toure by Rojo.
The visitors were then forced into another change, Rojo suffering a shoulder injury and having to be replaced by 19 year-old Northern Irish centre back McNair.
Ten minutes later Toure's pass sent Clichy to the byline and he cut the ball back for Aguero to hook in his 10th league goal of the season.
Forced to push forward, United finally threatened for almost the first time.
After 70 minutes, Joe Hart had to save at the near post from Robin van Persie and shortly afterwards he denied Angel Di Maria.
That followed a driving run by Wayne Rooney, back in the side after missing three matches through suspension, who had been adopting a deep-lying role even before the sending off.
Fellaini was then guilty of a bad miss, heading wide from close range in United's best spell of the game.
Sending on Edin Dzeko and Sami Nasri for Stevan Jovetic and Milner failed to give City any fresh impetus, although Navas did hit the outside of a post.
City were relieved to hear the final whistle as captain Vincent Kompany admitted and said: "You miss a couple of chances and seem to lose a little control. They played well towards the end. But we stayed strong for a clean sheet and a good derby win."              

Fellaini not a 'spitting figure', says Van Gaal

Louis Van Gaal defended Marouane Fellaini against suggestions that the Belgian midfielder may have spat at Manchester City's Sergio Aguero during the derby at the Etihad Stadium on Sunday.
Social media was left abuzz, speculating over whether footage of a first half incident in which Fellaini stood over the fallen Aguero, accusing him angrily of having dived in the area, also featured him spitting at the Argentine striker, City's match-winner in the 1-0 win.
Yet United manager Van Gaal insisted that Fellaini was not a "spitting figure" and that viewers of the incident may have actually seen merely a tirade of anger from his player.
Fellaini had certainly been enraged by Aguero's tumble in the box under his challenge, turning to remonstrate angrily with him after the referee Michael Oliver had turned down the appeal.
"I've heard that it is a question on social media but already that if he (Fellaini) is shouting and sometimes when you shout, there's a little bit of - how do you call it, saliva? - with it. I don't think he's a spitting figure," said Van Gaal.   

'Not too smart' Smalling dismays United's Van Gaal

Meanwhile, it was a wonder that Louis Van Gaal's face did not turn as scarlet as his team's shirts.
After preaching the need for discipline and calm-headedness in the furnace of the Manchester derby on Sunday, all the new United manager got for his pains was the match-losing brainlessness of Chris Smalling.
There could be little argument that at a moment when United's defence, which has looked so rickety and vulnerable all season, needed proper resolve in a game low on quality and high on passion, it was undone by the England defender's two yellow cards, which ultimately proved the key for City's 1-0 triumph.
On Friday, Van Gaal had made it clear that he expected the right form of self-control from his players on his Manchester derby debut, if they were to arrest the sequence of five City wins in the previous six Premier League meetings.
"We don't want a red card because when it is 11 v 10, it shall be very difficult to win this game. So that is also part of our preparation," had been his public warning.
So how did Smalling respond to this message?
First, in the 31st minute, when trying to stop Joe Hart with ball in hand from making a swift clearance from his box, he muscled in to block the quick delivery and received a quite needless yellow card.
Then, just before halftime when United seemed to have weathered City's storm of attacks, which saw David de Gea making one brilliant save from Jesus Navas and one extremely brave one from Sergio Aguero, Smalling stormed in to intercept a James Milner run down the left both late and recklessly.
He had to go.
"The first (yellow card) I didn't see. I don't know why the referee has given it but as a player when you have a yellow, you have to deal with it, you know that,” Van Gaal said.
"You cannot do what he (Smalling) did for the second one. It's not very smart. What can I say?" shrugged Van Gaal.
Smalling had shown humility when apologising to his team mates, the Dutch coach told reporters.
"You can only accept it (the apology). Nevertheless, in my opinion, this (the second yellow) is not so smart,” he added.
Not so smart? It was a good job perhaps then that Van Gaal had missed the original yellow card offence, which had immediately put Smalling under untold pressure.

Once Marcos Rojo also had to come off with a dislocated shoulder early in the second half, it meant United were reduced to repelling the waves of blue attacks with one of the weakest-looking back fours they can have ever fielded in the Premier League.
"As a coach, you can be proud of the last 20 minutes because they showed unbelievable willpower in my opinion. We could have scored at that moment," the Dutch said.
Ultimately, though, willpower was again not enough. City manager Manuel Pellegrini, happy purely to have avoided all the pre-match muttering about the prospect of him losing back-to-back league matches with the champions for the first time, reckoned the result was all that mattered.
He would not even bring himself to criticise referee Michael Oliver for the failure to award any of the three penalty appeals involving Aguero and Toure.
"It's a very difficult profession being a referee," he said, understandingly.    (Reuters)
Rojo has dislocated shoulder, United confirm
Argentina defender Marcos Rojo dislocated his shoulder in Manchester United's 1-0 defeat at Manchester City on Sunday, Van Gaal confirmed.
"His shoulder is out," the Dutchman told reporters.

"We don't know how long that will take. I have to wait until Monday. But he shall not play against Crystal Palace (on Saturday), I don't think,” he added.
Rojo, who joined the club from Sporting Lisbon in August, fell heavily in a collision eight minutes into the second half and had to be replaced by teenager Paddy McNair.  

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