The Blues dominated large parts of the game and took the game to a United side that were unbeaten in 40 home games and had a 100% home record this campaign.
Silva stabbed home from close range just before the break and though Marcus Rashford levelled moments later, Otamendi’s fifth goal of the season on 54 minutes proved to be the winner in a match that fizzed and threatened to boil over on a number of occasions.
City started as they meant to go on, bossing possession and seeing most of the ball while United sat back and soaked up the pressure.
Kyle Walker was cautioned after just five minutes for a challenge on Ander Herrera as referee Michael Oliver set an early precedent for any challenges deemed borderline.
With the Reds allowing the Blues to dominate the ball, it was inevitable there would be a presentable chance sooner or later and on nine minutes Raheem Sterling’s clever pass found Gabriel Jesus close to goal - but the Brazilian’s attempt at a back-heel to Silva failed to find its mark.
Then City almost breached the stoic Reds’ rear-guard when Fernandinho drove forward and played a superb pass down the channel for Jesus to comprehensively beat Marcos Rojo, before shooting tamely at De Gea.
The Blues seemed to be just one pass from breaking through on a number of occasions, but United defended well and as half-time approached, it appeared the opening period would end goalless – then, City finally broke through.
A Kevin De Bruyne corner was accidentally deflected goalwards by Romelu Lukaku and Silva was the first to react, putting the ball to the left of De Gea to give the Blues a richly-deserved lead.
It had been coming and the Reds could have no complaints at that stage, given the balance of play.
Moments later De Bruyne ran at the United defence again as the Blues counter-attacked with pace, but Sane’s run inside meant the Belgian’s pass went behind the German winger and the hosts escaped further punishment.
Deep into added time and against the run of play, however, United equalised.
A deep cross into the City box looked hopeful rather than anything more, but the ball flicked off the head of Otamendi and skimmed past Fabian Delph to Marcus Rashford who drilled home an angled shot to send the teams in level at half-time.
It was harsh on the Blues, but evidence that even a split-second loss of focus could be punished by a United side rich in attacking talent.
Vincent Kompany failed to appear after the re-start and was replaced by Ilkay Gundogan with Fernandinho dropping into the back four alongside Otamendi.
The Blues resumed control of proceedings in the early stages and took just nine minutes to retake the lead – and again Lukaku was heavily involved as De Bruyne’s free-kick was whipped in and the United striker’s clearance cannoned off Herrera. The lurking Otamendi spectacularly volleyed home from close range.
It had been an almost identical goal to the Blues’ first and not the sort of determined defending that the Reds have become known for under Jose Mourinho.
City came close to a third goal on 63 minutes following brilliant work by the ever-impressive Silva who drove into the Reds’ box, calmly played it to the overlapping Gundogan who played it invitingly across the six-yard box… but there was no City player in sight.
Then, on 70 minutes, De Bruyne forced a fine save from De Gea as both sides traded blows at either end.
United came close again as Rashford almost capitalised on Delph’s misjudgement and forced a good save from Ederson on 76 minutes as the hosts attempted to build up a head of steam.
Herrera was booked for diving after falling over an Otamendi challenge in the box as the game entered a frantic final ten minutes.
And it looked certain that the Reds would draw level when Anthony Martial volleyed a low cross into the path of Lukaku who fired a shot in from point-blank range but Ederson produced a superb double save, first from the Belgian then from Juan Mata.
It was as brilliant as it was brave by the young Brazilian and arguably, a match-winning double stop.
In the closing minutes, City had several chances to put the game to bed – a couple fell to Bernardo Silva – but none were taken ensuring fingernails continued to be bitten until referee Oliver called a halt to proceedings and the celebrations began on and off the pitch.
A fantastic win and a deserved one for a City side who continue to break domestic records.
Ederson’s brilliant double save, the first with his face and neck and the second low to his right earned the Blues all three points.
A goal for United at that stage would have most likely led to a late onslaught from the Reds and who knows what could have happened?
Star man: David Silva
A display that had everything – a goal, resilience, fight and great leadership.
What it means…
City go 11 points clear of second-placed Manchester United.
City travel to South Wales to take on 19th-placed Swansea at The Liberty Stadium.
Then it’s back to the Etihad and another tough game against Tottenham Hotspur next Saturday.
Stats and milestones:
City’s start to the 2017/18 campaign is the best ever in the Premier League.
The Blues have now won nine Premier League away games in succession.
City have recorded the most successive wins in a single season in Premier League history – 14. Arsenal have also won 14 Premier League games in a row, though this was over two campaigns.