The hosts started brightly, with Louie Sibley firing inches wide, but it was Shaw who opened the scoring with a bouncing strike that looped over Derby 'keeper Kelle Roos, before Ighalo struck twice -- taking his United tally to three in two starts -- to seal victory.
This was the fifth domestic meeting in just four years between the two sides, but Wayne Rooney's United reunion added some extra spice to a familiar tie on a chilly evening in Derbyshire. The Derby skipper was desperately close to grabbing a memorable goal too, but Sergio Romero produced two fine saves from free kicks as United booked a quarter-final tie with Norwich.
United weren't faultless but, despite a couple of spirited Derby spells, they were largely dominant. The visitor's continued their longest unbeaten run of the season -- now at nine games -- breezing into the next round, while Ighalo made it three goals in three to continue his bright start at Old Trafford.
The visitors looked fragile in the early stages as Derby's fearless teens fired a couple of warning signs. Meanwhile, a slow start to the second half could have invited Derby back into the contest, only for a few narrow misses. It was also an unhappy 27th birthday for Harry Maguire who earlier limped out of training.
Manager rating out of 10
7 -- Ole Gunnar Solskjaer made six changes, including bringing back cup specialist Sergio Romero in goal and starting Ighalo up top. Those changes proved to be a good call as the latter's second and third goals in United colours went unanswered.
Player ratings (1-10; 10 = best, players introduced after 70 minutes get no rating)
GK Sergio Romero, 8 -- Suffered an early scare when Sibley's ferocious left-footed strike flashed just past the post, but twice produced a strong right-hand to deny Rooney a sentimental wonder goal. Thwarted Jack Marriot with another smart stop.
DF Diogo Dalot, 5 -- Far too hesitant when Sibley burst forward, which seemed to leave Shaw feeling obligated to hack the youngster down. Cleverly span away from his marker at the other end only for Juan Mata to blast his cross behind.
DF Victor Lindelof, 6 -- Brought in for the injured Harry Maguire, but the centre-back didn't have too much involvement in a relatively scare-free affair, That said, he made a routine stop slightly more difficult for Romero when Max Bird's effort awkwardly struck his foot.
DF Eric Bailly, 6 -- Hooked away Max Lowe's cross on the slide as the hosts started with a buzz, but later allowed Martyn Waghorn to get across him and glance an effort just wide. Booked for clattering into Sibley.
DF Luke Shaw, 8 -- The left-back went into the book for a completely avoidable challenge on Sibley, but produced an energetic display against youthful opponents. He put United ahead -- possibly via Jesse Lingard's back -- with a strike into the ground that looped over Roos and assisted Ighalo to double the advantage with a smart ball into the striker's feet.
MF Scott McTominay, 6 -- The Scot was surprisingly careless in the opening seconds when he moved swiftly to halt a Derby break only to completely miss the ball. He was treated to a crunching Rooney tackle shortly after, before dishing out some fire of his own as he continued to give Sibley a piece of his mind following a coming together.
MF Fred, 6 -- The Brazilian has been brilliant this year but this wasn't his best display. He conceded a few cheap free kicks in a tired performance that featured some equally lethargic passing. Did show brilliant feet to skip past two challenges in the lead up to a Mata effort.
MF Juan Mata, 6 -- Had to wait until the 27th minute for his first involvement of note, but his low shot was watched all the way by Roos. Hit the target again with an ambitious, floated attempt from range, but the goalkeeper had plenty of time to scramble back to his line.
MF Bruno Fernandes, 7 -- No goal this time, but Fernandes has completely lifted United, who craved his creativity prior to his arrival. "Bruno" was once again affectionately chanted from the stands as the Portugal man continued to pick out dangerous areas with calculated passes.
MF Jesse Lingard, 7 -- The midfielder showed plenty of urgency and enthusiasm, but that was curbed slightly by an accidental kick from Bird. A spirited display if not an exhilarating one from the Englishman who had Roos scrambling with a late effort.
FW Odion Ighalo, 8 -- He just loves scoring on Thursdays. Three in two starts now for the Nigerian who squeezed his first effort into the left corner, before hammering home his second much more emphatically -- albeit it at the second attempt. Would have had a hat trick only for a vital Roos save in the first half.
DF Brandon Williams, N/R -- Replaced man of the match Shaw but had little influence.
MF Andreas Pereira, 6 -- Came on for Fernandes in the 67th minute and quickly found a sight of goal, but struck his effort comfortably over.
FW Anthony Martial, N/R -- Replaced birthday boy Fred in the 73rd minute but the game had settled down by that point in truth.