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.
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.