Right, that's it for the night. See you all in the morning. 

Image source, Getty Images

Derby manager Paul Clement: "You're always worried about those quality players, like Mata and Martial, off the back of our midfield. They were clinical, their movement and finishing was the difference. 

"I thought we gave them a good game, it wasn't an easy game for them. We had some good passing spells and our goal was an excellent goal, a good finish from our holding midfielder - although I don't know what he was doing up there!

"I'm disappointed we didn't keep it tighter for a bit longer so we could go into the last 15/20 minutes with a chance. For a team who is lacking confidence they played well tonight."

Game, set and match.

Robbie Savage
Former Derby midfielder on BBC One

“I was slightly disappointed in Derby to be honest. They did sit off and didn’t get after Manchester United. They have got a massive game against Preston on Tuesday and having spent £25m it is more important for them to get into the Premier League."

Manchester United

Image source, Reuters

Manchester United manager Louis van Gaal: "It was maybe better than we had trained. We played at the right time against the resistance of Derby. We gave their goal away but at half-time I said that it was a good performance, keep it up and we will win. And we did.

"Daley Blind's goal? You have to sniff it and he sniffed it. It was a great goal. The Premier League is very important but the FA Cup is the greatest cup in England with a long and important history. We haven't won it for a long time so we dream of it. After two wins you can't say that we will win it.

"What did I write down when Daley Blind scored? Who gave the assist."

Derby boss Paul Clement is quick to turn his focus back to the race for the Premier League, saying "there are 18 games left."

Image source, Reuters

Thomas Fawcett: If Man Utd can play in that fashion, on the front foot with players pushing forward, then top four is a certainty!

Eteyen Adegoke: Martial and Rooney excellent, but how about Varela? Outstanding performance from the youngster! Hope he can kick on.

James: Positives: Utd can still score goals, Martial, Varela and Borthwick-Jackson, FA Cup 5th round. Not bad.

Buttsy: Fellaini is the worst player I have ever seen in 64 years of watching United.He wouldnt get in my pub team.

Buttsy?! Surely Nicky Butt's dad hasn't text in...

Two of Manchester United's goalscorers have been chatting to BBC Sport's Dan Walker in the iPro Stadium tunnel. (Clue: Wayne Rooney isn't there.)

Juan Mata: "It was really important for us to win. It is not easy to come here, even though they are not in the Premier League, they are a good team and are physically strong, like to press, and I think we did a good job. We came here to play football and play quicker and create more chances to score."

Daley Blind on his goal: "I made a move forward and when I was in the box I thought I should go to the front post like a striker does and it was a perfect ball. We did what we needed to do and that was win."

Image source, Empics

Peter Schmeichel
Former Manchester United goalkeeper on BBC One

"If they had lost tonight, Manchester United's season would have been over. And when was their season ever over in January?"

Big money, big problems for Derby. Anthony Martial may be slightly blunted out wide but he still set up two goals tonight.

Robbie Savage
Former Derby midfielder on BBC One

"Wayne Rooney has scored so many important goals for Manchester United in recent weeks. Tonight he got the ball rolling with a magnificent finish."

Been out schmoozing and missed Rooney's opener? Watch it again here.

Derby have now lost three games on the spin and only won one in seven - at Hartlepool. Can the Rams get their promotion bid back on track? They face Preston on Tuesday. 

Peter Schmeichel
Former Manchester United goalkeeper on BBC One

"I'm not going to say it was a brilliant performance by Manchester United but it was so much better than recent weeks. It gives you hope that something better is around the corner."

Robbie Savage
Former Derby midfielder on BBC One

"Derby were in with a chance at 1-1. But let's not get carried away by United - they've won against a Championship side that hasn't won for five games."

Alan Shearer
Former England striker on BBC One

"I thought Manchester United dominated in the second half and never gave Derby a sniff. It was a professional performance. I thought Martial and the two young full-backs were superb."

Manchester United are the first team into the hat for round five then. That draw takes place on Sunday evening.