Erling Haaland set the Blues on the way with a first-half penalty that was scant reward for the dominance showed.
The Norwegian headed home his second just after half-time before setting up Phil Foden for a late third.
It was no more than the Treble winners deserved after what was a stunning 90 minutes against our cross-city rivals.
Before kick-off, there was an emotional tribute to Sir Bobby Charlton, with Mike Summerbee and Tony Book representing City – as well as Brian Kidd who played for both – warmly welcomed onto the pitch before a minute’s applause echoed around Old Trafford.
The game began with the Blues initially looking a little disjointed before finally getting into a rhythm and almost taking the lead on eight minutes.
In fact, the only surprise was the ball not ending up in the United net as Rodrigo’s lofted pass found Kyle Walker’s run into the box and the City captain’s header found Phil Foden who in turn saw his header pushed out by Andre Onana, but only toward Haaland who tried to connect with his foot instead of his head and somehow United scrambled the danger away.
The hosts' tactics were to get numbers in behind the City midfield and their counter-attacks were looking dangerous, with the Blues’ defence outnumbered on a number of occasions.
The next effort of note by City was a curling shot by Jack Grealish on 20 minutes that Onana turned around the post.
City continued to press and Foden won a free-kick 35 yards from goal.
The official went to the pitchside monitor and decided Rodrigo had indeed been fouled and pointed to the penalty spot.
Haaland, getting stick from the Stretford End, kept his nerve and sent Onana the wrong way to make it 1-0 - it was our first penalty at Old Trafford since 1992, so it had been a long time coming!
The remainder of the half saw the Reds pegged back in their own final third as City dominated possession, often with the outstanding Rodrigo pulling the strings.
Yet the home side fashioned a terrific chance to level in first-half added time as Scott McTominay finished a counter-attack with a fierce rising shot from the edge of the box that Ederson superbly turned past the post.
City responded with what should have been a second goal after a patient build-up ended with Bernardo’s deft cross from the left finding the head of Haaland, but the striker's decision to plant the ball centrally allowed Onana to make a point blank save.
That was the last act of a half that the Blues should have been two or three goals to the good.
United were quickly on the attack after the restart with Bruno Fernandes firing a vicious swerving drive that was again superbly dealt with by Ederson.
A couple of minutes later and those small margins were exploited as the Blues doubled the lead.
A purposeful break forward saw Alvarez switch play, finding Grealish on the left – he waited for the overlapping Bernardo and again the Portuguese sent in a pinpoint cross that Haaland firmly planted home to make it 2-0.
The impressive Grealish was denied by Onana on 55 minutes with Bernardo’s dashing run on the left creating a gap that the England winger almost exploited.
City were purring and United were chasing shadows at times, but there was always that feeling that should the home side find a goal, it would be a different game.
And that danger was illustrated with a rare United attack on 69 minutes almost resulting in a goal as Marcus Rashford ghosted into the box unmarked and after cushioning the ball on his chest, he just sent an angled shot wide.
Two minutes later Grealish threaded a ball though to Haaland in the box, but Onana clawed his shot out for a corner.
The goal that finally settled the points - not that there had ever really been any doubt since the second strike - came on 80 minutes when Haaland unselfishly picked out Foden's dart into the six-yard box and the England playmaker coolly flicked home to make it 3-0.
United players picked a plethora of late bookings, losing their discipline as City gave a statement performance in the Manchester drizzle.
It was a wonderful, vibrant 90 minutes from Guardiola's side.
MAN UNITED XI: Onana, Dalot, Maguire, Evans, Lindelof (Reguilon 74), Amrabat (Mount 46), McTominay, Eriksen (Antony 86), Fernandes (c), Rashford (Martial 86), Hojlund (Garnacho 74)
Subs: Bayindir, R. Varane, , Hannibal, Mainool
Subs: Ortega Moreno, Phillips, Aké, Gómez, Nunes, Bobb, Lewis
Pep Guardiola reaction
On the performance:
“The second goal helped us a lot. We talked at half-time.
“After we dropped. We made a good action and that was the key point of the game.
“First seven minutes we lost the ball because we didn't do simple things.
“We allowed them to make a transition. The second half was brilliant.
“Last season we lost, this season we won, and it is always special to win at Old Trafford. We are so proud."
“No tattoos or nice car. An incredible player for us. He loves to play at Old Trafford.
“He's played as false 9 in the past and he has the ability to make a lot of passes.
“So intelligent… everyone loves him and another exceptional performance.
“He's one of the best players I’ve ever seen in my life. I've trained a lot and he's one of the best.”
Man of the Match
Bernardo Silva was magnificent from start to finish.
He mixes intelligence with skill and a fantastic workrate that starts from minute one and ends at minute 90 (plus added time!)
He continually provided support down the left flank for Grealish and his passing selection was outstanding.
Haaland should have headed the first chance the Portugal star created home on half-time, but made no mistake with the second carbon copy cross he sent in after the break.
But those chances only told half the story for a player who was involved in everything and seemingly omnipresent throughout.
“It was a good game for us today. Apart from a few simple balls that we lost, we didn’t give them much to counter and the way we controlled the game.
“The first 30 minutes of the second half we were really good. What we lacked against Arsenal in the pressing we had it today, we were fabulous.
“It’s not easy to play here at Old Trafford. Congratulations to the big man for the two goals and the assist.
“When we come to these types of places, Anfield, Old Trafford, we know what teams are waiting for. For us to lose the ball and counter.
“It’s all about the build-up, not losing the simple balls, controlling the game and being slow in the first metres of our half, in goal kicks and in our half of the pitch and when we break through, be quick and attack.
“That’s we did really well in the second half. So happy with the performance. So happy with the three points. It’s never easy to come here and beat this team.
“It was amazing. A fantastic win. The game was incredible today, the whole team and everything, especially Bernardo, were impressive today.
“For my assist, I saw Phil was alone, so it was simple as that.
“I felt it (nervous) a little bit for the penalty. A lot of people were singing to me ‘Keano’ -.I don’t know why.
“It is what it is. I had the pressure and I scored, and it was a fantastic feeling. It was a nice celebration, for both of them. It was a nice game.
“Onana made an incredible save right before the half time. He did another fantastic save in the second half when I chipped it, he saved it with his head.
“It is what it is. We won. I don’t care.”
What it means...
City are joint second in the Premier League table after this victory.
The Blues are equal on points with Arsenal and both sides have a goal difference of +15.
Spurs continue to lead the table by two points.
City have a rare blank midweek following our exit from the Carabao Cup.
That will give Pep Guardiola time with his players ahead of next Saturday's clash with Bournemouth.
The Premier League fixture will kick-off at 15:00 (UK).
Stats and facts
- City have won more Premier League away games against Manchester United than any other side (9), with eight of our last nine wins at Old Trafford coming in their last 13 visits.
- Since the start of the 2011-12 season, City have won 14 of our 25 Premier League meetings with Manchester United (D3 L8), more than any other side in that time. Their previous 13 league wins over the Red Devils had come over a 62-game period between 1970 and 2011.
- Only Arsène Wenger (12) has ever won more Premier League games against Manchester United than City boss Pep Guardiola (8). Of all managers to have faced the Red Devils at least 10 times in the competition, Guardiola is the only one to have won more than 50% of his games against them (8/15).