The Premier League side extended their unbeaten run in all competitions to nine games – ahead of Sunday’s derby visit of rivals Manchester City – and remain in the hunt for the FA Cup, Europa League and a top-four finish in the Premier League.

Solskjaer said: “I’m very pleased with the performance and to go through. You never know, away from home, being the favourites and having City on Sunday how it’ll affect their mindset – but it was professional.

“Thursday was the highest priority because we’re not going to pick and choose games or competitions. We have to go for everything, that’s what it is to be at Manchester United.

“It’s another away draw, we’re used to that now. Is it a seventh in a row? We’ll have to do it the hard way if want to go all the way. We’ve got a chance now.

“We’ve found form and defended well, we’ve had seven clean sheets in those nine games.”

United are chasing a record-equalling 13th FA Cup triumph but survived two early scares when Louie Sibley shot wide and Romero saved Rooney’s free-kick.

But the visitors took control at Pride Park after 33 minutes when Shaw scored just his second career goal, his volley bouncing over Kelle Roos.

Ighalo made it 2-0 seven minutes later when he held off Craig Forsyth and found the corner, while Martyn Waghorn went close for Derby after the break but Ighalo ended the contest when he fired home with 20 minutes left.

Solskjaer added: “He’s doing what he says on the tin and what we asked for when we signed him. I’m very happy with him. That type of striker is vital for a team.

“There’s more to come, he’ll improve and get sharper and more used to us. I’ve got no doubt he’ll only get better and better.”

Rooney almost grabbed a consolation but Romero produced an excellent stop to turn his late free-kick over.

Rams boss Phillip Cocu said: “If the first free-kick goes in, sometimes it defines a game.

“You have to be really effective and on that side they were much better than we were.

“I’m quite satisfied with the performance.”