United’s all-time top scorer was the centre of attention as the Rams skipper looked to help the mid-table Championship side spring a surprise at a sold-out Pride Park.
But Derby’s bright start petered out as United’s superior quality showed through, with Luke Shaw’s second career goal complemented by January signing Ighalo’s brace in a comfortable 3-0 win.
Much-changed United eventually settled and took a two-goal lead into the break, with Shaw’s volley into the ground looping over Kelle Roos before Ighalo coolly turned past the Derby goalkeeper.
The Rams’ dreams of a first quarter-final appearance since 1999 evaporated with Ighalo’s second of the night during a second half that saw the raucous away support serenade their former star Rooney.
Victory extended United’s unbeaten run to nine matches in all competitions, but Phillip Cocu’s men made it hard for the visitors early on.
Jason Knight’s cross was begging to be turned home two minutes later as the Rams continued to push forward, with Shaw booked for a mistimed recovery challenge on lively Sibley.
Rooney stepped up to the resulting free-kick and would have put Derby into a dream 18th minute lead had Romero not impressively got across to claw behind his curling attempt.
United had yet to create a clear chance as their final ball was either lacking or blocked, with it taking until the 26th minute for Juan Mata to send a low effort that Roos gobbled up.
The Derby goalkeeper made himself big when Ighalo was put through as Solskjaer’s side began to up the ante, turning the screw until the pressure told in the 33rd minute.
Jesse Lingard and then Bruno Fernandes saw shots blocked, with Shaw volleying the loose ball into the ground with enough to power to see it loop up and out of Roos’ reach.
It proved a gut punch Derby were unable to recover from.
The lack of video assistant referee at this match saved George Evans after clearly handling a Fernandes strike, but United would only be momentarily held off as Shaw added an assist to his goal.
The left-back ran through before playing in Ighalo, who cut past Craig Forsyth and Max Lowe before squeezing an effort into the bottom left-hand corner to the elation of the lively away support.
Tom Lawrence soon went off injured to compound matters, with Derby’s frustration epitimosed by the challenge that saw Rooney booked just before the break.
Derby, much like the first period, started the second half on top.
Max Bird had an attempt before Martyn Waghorn glanced a header just wide having connected with a fine Jayden Bogle ball.
But the hosts’ attempts to reduce the deficit left gaps.
Shaw, McTominay and Mata had shots before Ighalo added gloss to the scoreline. Undeterred when his initial effort was cleared off the line by Bogle, he rifled home the second attempt with 20 minutes remaining.
Jack Marriott and Knight saw late efforts stopped by Romero, who did superbly to tip over a stoppage-time Rooney free-kick after Ighalo went close to his hat-trick at the other end.