Bernardo Silva thumps into top corner from 25 yards & slips in Mahrez for second before Pereira own goal
Rashford finishes breakaway for Man Utd response
Man City and Man Utd won the last four EFL Cups between them
Second leg on 29 January - winners play Villa or Leicester at Wembley
Image source, Getty ImagesIf you're just tuning in wondering how the Manchester derby went down - it was a convincing win for the boys in blue.
You can read Chris Bevan's match report here, and scroll down for all the big reaction from Old Trafford.
The second leg is to come on 29 January, while you can join us tomorrow night for Aston Villa v Leicester.
Until then!
One good result tonight - just one arrest made at the derby.
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The last 15 teams to win away from home in the first leg of the League Cup semi-final have all progressed to the final, with the last side to fail to do so Spurs against Arsenal in the 1986-87 season.
Manchester United 1-3 Manchester City
Manchester United
Image source, Getty ImagesManchester United boss Ole Gunnar Solskjaer on Sky Sports: "From their first goal and especially the second we struggled to get to grips with them. A good reaction second half, but first half until they scored it is was back and forth. We didn't cope with the setback well enough.
"We didn't deal with their system well enough, we know they can play that way. They played that way last season and beat Chelsea 5-0.
"First goal there is nothing we can do, second is sloppy and the third we just didn't recover.
"With Matic and his experience (coming on in the second half) he had more presence. It was more about wanting the ball and believing, passing the ball. Someone needed to take responsibility. We've shown before we have been down from a home tie and turned it around. PSG is the latest example and we have to believe that we can put on a performance.
"It was a decision late on on who was fit, it was no excuse. We have the players we have. We put a team out believing we could get a result."
Image source, BBC SportA clear winner in your votes - Bernardo Silva clocking 7.86. Well deserved.
See all of your ratings here - two players for Manchester United scored under three...
Leicester v Aston Villa (20:00 GMT Wednesday)
Brendan Rodgers wants Leicester to "create new history" by reaching the Carabao Cup final with victory over Premier League rivals Aston Villa.
The Foxes, who last won the trophy in 2000, host Villa in the first leg of their semi-final on Wednesday.
"I'm aware the club hasn't been to a final for 20 years so let's get there then," Rodgers said, with his side strong favourites.
Manchester United 1-3 Manchester City
Manchester City
Image source, Getty ImagesMore from Manchester City boss Pep Guardiola on BBC Radio 5 Live: "The last game (a 2-1 loss in December) we could not control when we lost the ball and tonight we did it better.
"We lost the ball in a position which is so dangerous (for the United goal). We cannot forget which team we play. Tonight we can be more than satisfied to come here to Old Trafford and win.
"It is not over. We have one more game and we'll see what happens.
"Of course Manchester United can come back. Last year here they lost to PSG and they qualify (in the Champions League). They have the shirt which means history and pride."
Pep Guardiola loves a post-match chat. Loves it.
Manchester United 1-3 Manchester City
Manchester City
Manchester City manager Pep Guardiola: "The first minutes were tight but then we had an outstanding goal and we played really good. In the second half they changed their shape and we struggled a little bit to keep the ball.
"It's not over because it is United, they are able to score goals but hopefully we can reach the final again.
"It is hard to control Rashford because he is so fast so we are comfortable with the ball so we played many passes. Bernardo always plays good he is a fantastic footballer.
"We play United, what do you expect, a 7-0 win? In general it was an incredible performance at Old Trafford."
Manchester United 1-3 Manchester City
James Ducker
The Telegraph's Northern Football Correspondent
If United look at that with cold logic they will see it as a wake-up call. That is the bar that has been set by City and Liverpool.
United as a club expect to win trophies, that is the reality they have to face. United need so many players it will be a slow climb back up.
Manchester United 1-3 Manchester City
Manchester City
Image source, PA MediaManchester City boss Pep Guardiola is asked on BBC Radio 5 Live about a "masterclass" move to play without a number nine.
"Why is it a masterclass?
"I would like to know what people say at the beginning when we play without Sergio Aguero and Gabriel Jesus. We win and we're a genius but if we don't win I know what will happen. We try to control the counter attacks because they're a wonderful team."
Image source, BBC SportRobbie Savage isn't happy with United players getting twos and threes but you can have your say - head over here to rate the players out of 10.
#bbcfootball or text us on 81111 (UK Only)
Ole just isn't good enough, however nice he is. Everyone saying give him more time is just being sentimental. Tactically inept. It's like having a boss you love but they just don't understand the job. I've said it from the start.
Dave, Manchester
Pep Guardiola is told on 5 Live that he put on a masterclass and he's not happy about it.
"Why? Why is it a masterclass?"
A hard man to please at times...
Manchester United 1-3 Manchester City
Manchester City
Manchester City right-back Kyle Walker on Sky Sports: "I saw space and if i see it I'll attack it. The first half was great and second half they changed the system. Fair play to us we got the result we needed and on to the Etihad now.
"We knew they'd come out differently, it was about controlling the game as much as possible and saving your legs as best you can."
#bbcfootball or text us on 81111 (UK Only)
Alan McDonald: Just need a PSG-style return leg now and we're all good. Simple.
Ilyas: The Rashford goal shouldn’t be used to paper over the cracks at Old Trafford, tonight has been an embarrassing one for Man Utd and if things carry on like this, Ole won’t be at the wheel next season.
Manchester United 1-3 Manchester City
Image source, Getty ImagesManchester City midfielder Bernardo Silva to Sky Sports: "We could have gone in four or five up at half-time, we had the chances. They pressed us higher in the second half, we got tired but overall we are happy.
"I enjoyed my role - because it worked and we won. Pep wanted one more man in the middle."
Robbie Savage
Ex-Wales midfielder on BBC Radio 5 Live
Image source, Getty ImagesManchester United were better in the second half, they got to grips with that City shape. Ole Gunnar Solskjaer brought on Matic and went to a 4-3-3 which really helped them.
They've won the second half and as manager you want a reaction from your players and he got that.
Of course it will hurt - it's a derby and a semi-final. Outplayed and outfought and they were better second half.
Guardiola has come up with a plan to beat Manchester United once again. This was another masterclass from Pep.
Manchester United 1-3 Manchester City
As 60-odd thousand people empty out into the streets of Trafford the City fans stay up in their corner singing and dancing. League Cup or not, a derby day win away form home is always one to savour.
Robbie Savage
Ex-Wales midfielder on BBC Radio 5 Live
City seemed to have played in second gear in the second half. United were outplayed in the first half, they have shown their manager a reaction. I can't see United going to the Etihad and repeating the 2-1 win from December, which still wouldn't be enough.