Odion Ighalo scored twice as Manchester United eased to a 3-0 win at Derby and into the quarter-finals of the FA Cup.
Wayne Rooney's presence in the Derby team dominated the build-up but Luke Shaw's opener and a goal in each half from Ighalo took the game away from the Championship side.
The win extends United's unbeaten run to nine games and with a last-eight tie against bottom club Norwich to look forward to there will be hope of FA Cup glory in May.
Rooney was Manchester United captain the last time that the club lifted the trophy in 2016 but he had only a booking and a warm reception to show for his efforts on a night when his new team were outgunned.
Derby County: Roos (6), Bogle (6), Forsyth (6), Evans (6), Lowe (6), Knight (6), Sibley (7), Bird (6), Rooney (7), Lawrence (6), Waghorn (6).
Subs:Whittaker (6), Marriott (6), Shinnie (6).
Manchester United: Romero (8), Dalot (7), Lindelof (6), Bailly (7), Shaw (8), Fred (7), McTominay (7), Mata (8), Fernandes (7), Lingard (6), Ighalo (8).
Subs: Pereira (6), Martial (6), Williams (6).
Man of the Match: Odion Ighalo
How Man Utd progressed to the quarters
Derby, mid-table in the Championship, had hoped for better having come into it unbeaten in front of their own fans since before Christmas and there were positives early on.
Louie Sibley fired a left-footed shot just wide of Sergio Romero's post inside 10 minutes to get the home support involved and Rooney himself went close soon after.
After Sibley had been cynically fouled by Shaw, United's all-time top scorer whipped in a free-kick that looked likely to creep in at the near post only for Romero to push wide.
But much of the slicker work from the outset came from the Premier League team with Bruno Fernandes and Juan Mata at the heart of United's good build-up play.
A poor touch from Max Lowe allowed Ighalo to sneak in between two markers but his powerful shot struck goalkeeper Kelle Roos and Derby went unpunished.
Kelle Roos returned to the Derby team as their FA Cup goalkeeper, while Max Lowe, Louie Sibley and George Evans all returned to the side too. The big news, however, was that Wayne Rooney was in the starting line-up and wearing the captain’s armband against the club with whom he won this competition in 2016.
Sergio Romero and Odion Ighalo were restored to the team having also played in the 5-0 win over Club Brugge but Harry Maguire missed out at the back because of a minor problem. Even with a big game against Manchester City looming at the weekend, United named new favourite Bruno Fernandes in the starting line-up.
The shots kept coming and moments later United had their breakthrough goal.
Jesse Lingard and Fernandes both had efforts blocked in the same phase of play before Shaw's attempt bounced into the ground and over the head of Roos.
Pride Park was left stunned and Derby needed to regroup but instead, Phillip Cocu's side found themselves two down before the interval.
Ighalo showed great strength inside the penalty box before depositing the ball low into the corner of the net for his second goal in just his second start since arriving last month.
When Tom Lawrence was forced off injured, all hope seemed lost as the United fans sang of Wembley but Max Bird and Martyn Waghorn did go close early in the second half.
It was Solskjaer's side doing most of the pushing though with Fernandes' clever ball almost earning the impressive Shaw his second goal of the game.
Instead, it was Ighalo who became the two-goal hero after seizing upon Mata's pass and blasting the ball past Roos left-footed at the second time of asking.
There was still time for substitute Jack Marriott to force a fine save from Romero but any prospect of a comeback had long since disappeared by that point.
All that remained was for the visiting fans to hail their former hero Rooney and there was the tantalising prospect of some late excitement when Derby won a free-kick.
"If Rooney scores, we're on the pitch," chanted the away fans and it felt as if everyone in the ground wanted him to score - with the exception of Romero who tipped his fierce strike over the bar.
It was a night when Manchester United had one eye on the past - and another on a future trip to Wembley.
What the managers said
Phillip Cocu: "The difference in speed of passing, the limited time you have when you receive ball, for our team, and especially the youngsters, it was a great experience. In the end, you have to give credit to Manchester United. They deserved the win. They were much better than we were. But I think we deserved a goal."
Ole Gunnar Solskjaer: "I was very pleased with the performance and very pleased to go through. You never know away from home, being the favourites and having [Manchester] City on Sunday, how that will affect the mindset but it was professional.
"We have found form. We are defending well. Clean sheets, that's massive for us. It's seven in nine, that's important, and the two we have conceded we shouldn't have conceded. I have got good players and they are in form."
Live Renault Super Sunday
Analysis: Rooney Watch
Wayne Rooney would have dreamed of scoring the winner and upsetting Manchester United in his new home, but it wasn't to be for the Derby skipper.
There was adoration from all sides of the ground, with the visiting contingent from Man Utd particularly vocal throughout the second half. Rooney will know more than anyone, though, that it would have been different if his Derby side had been able to compete with their visitors.
That does not mean there were not moments of magic from Rooney and there were plenty of times you could see his quality on the ball, as well as the desire he's always had.
The two free-kicks were the moments when the crowd held their breath and just wondered if there was to be a standout moment, but that was not the only time he was at the centre of proceedings.
An early tackle brought a huge roar from the home crowd, while one later in the half stopped a breakaway United attack in its tracks and earned Rooney a booking. Far from the first of his career.
Shortly after tracking back into the box and intercepting a Bruno Fernandes ball that looked set to be swept home by Juan Mata, there was a wonderfully weighted ball between Victor Lindelof and Luke Shaw that found Jack Marriott, whose first-time effort forced Sergio Romero into a smart save.
Surrounded by fresh-faced teenagers, a 34-year-old Rooney is far different from the man who scored more than 250 goals for United during his time from Old Trafford. But as the visiting faithful labelled Rooney "The White Pele", there were moments when everyone remembered his glorious past.
Man of the Match: Odion Ighalo
After marking his first Manchester United start with a goal against Club Brugge, Ighalo's second start brought two more goals to see off Derby. The former Watford striker was derided as a panic buy before he had even kicked a ball but even panic buys can come good and the Nigerian has already shown what he can in front of goal.
"He is doing what it says on the tin and what we asked for when we signed him," said Solskjaer afterwards. "He is experienced and he has scored goals all of his career. He is in and around the box, he reads it, he sniffs out where the chances will come. I think that striker is vital for a team."
- Manchester United's victory means that all eight quarter-finalists in this season's FA Cup are Premier League clubs, only the fifth season to see the last eight remaining sides in the competition all from the top-flight, after 1894-95, 1895-96, 1995-96 and 2005-06.
- Manchester United have won each of their last nine FA Cup meetings with Derby County, a run of victories stretching back to March 1948.
- Derby County have failed to win each of their last 13 home games against top-flight clubs in the FA Cup when the Rams themselves were playing outside of the top tier (D5 L8), including three defeats to Man Utd in this spell.
- Manchester United are unbeaten in nine matches across all competitions (W6 D3), keeping seven clean sheets and conceding just two goals in total in this run.
Derby are back in Championship action on Sunday as they play host to Blackburn Rovers at Pride Park. That game is available on Sky Sports Football on the red button.
Manchester United are in action against rivals Manchester City at Old Trafford. That is a 4.30pm kick-off on Sunday with live coverage on Sky Sports Premier League from 4pm.