The Red Devils' January loan signing took his tally to three goals in two starts for the club after Luke Shaw had put the visitors in front on Thursday.
United's record goalscorer and former captain Wayne Rooney started against his old club but, aside from some impressing passing from deep, he could not help Derby spring a shock against Ole Gunnar Solskjaer's side.
There was some early threat to the United goal from Phillip Cocu's men, as Louie Sibley shot narrowly wide and Rooney saw a free-kick well saved by Sergio Romero.
United began to assume control, though, with Juan Mata and Ighalo denied by Kelle Roos, before Shaw broke the deadlock in fortuitous fashion 33 minutes in.
After Lingard and Bruno Fernandes saw shots blocked, Shaw fired a half-volley into the turf and, perhaps via a slight touch off Jesse Lingard, the ball looped over the stranded Roos and in.
Ighalo got the second four minutes before half-time, holding off the attention of Craig Forsyth and Max Lowe and poking the ball into the bottom-left corner.
Derby started the second half brightly and twice came close to a lifeline, with Romero saving Max Bird's deflected shot and Martyn Waghorn heading a fine Jayden Bogle cross inches wide.
Roos had to react well to deny Shaw and Mata, though, before Solskjaer took the chance to hand the excellent Fernandes a rest ahead of Sunday's Manchester derby.
The result was made safe with 20 minutes of normal time left, as Ighalo exchanged passes with Mata and, after seeing his first effort blocked by Bogle, rifled the rebound high into the net.
Rooney almost got on a scoresheet in front of the travelling fans, who chanted his name at several points in the match, but Romero made a flying save to tip his free-kick over the bar.
2 - Odion Ighalo has scored his first brace for an English club since netting twice for Watford against Liverpool in a Premier League tie in December 2015. Threat. #FACup #DERMUN pic.twitter.com/drz3K95TAe— OptaJoe (@OptaJoe) March 5, 2020
What does it mean? United building momentum for decisive few weeks
United are into the quarter-finals for the sixth season in a row, but that trip to Norwich City will be far from their minds as they look to continue their good recent form into a challenging run of games.
They face Manchester City on Sunday before a Europa League last-16 visit to LASK next Thursday, after which Tottenham and Jose Mourinho travel to Old Trafford before the second leg of their European tie.
With six wins and no defeats from their past nine matches in all competitions, Solskjaer will be hoping their momentum does not now fizzle out.
On Shaw footing
Shaw's form down the United left has been a real plus point of recent weeks, and it continued at Pride Park as he again showed his worth to Solskjaer. His miscued effort made his goal fortuitous, but his pass for Ighalo's second was excellent, and he nearly scored again after a promising run.
Sibley gets lucky
Sibley gave a good account of himself, but the 18-year-old may well have seen red for a kick at Scott McTominay's face had VAR been in use. The United midfielder was certainly unimpressed.
Key Opta Facts
- 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.
- United have won each of their last nine FA Cup meetings with Derby County, a run of victories stretching back to March 1948.
- Derby 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 United in this spell.
- Ighalo has scored in consecutive starts in all competitions for an English club for the first time since December 2015 for Watford, when he scored in four in a row; this was also his first brace for an English side since December 2015 against Liverpool for the Hornets.
United head to Norwich for the quarter-final on the weekend of March 21, but they have the more pressing concern of the Manchester derby on Sunday in the Premier League. Derby resume Championship duties against Blackburn Rovers on the same day.