The away side dominated the game early on and pushed back Alcorcon with some swift attacking football.
Fran Rico played a short free kick to create an opening on 16 minutes, but the defence blocked well.
Granada then took the lead just before the half-hour mark when Ighalo finished well from a Fran Rico free kick.
Three minutes into the second half, Hassan Yebda make a positive forward run, although the Alcorcon defence blocked as he tried to feed Ighalo.
The hosts tried to put pressure on the Granada defence, but they stood firm.
The away side withstood a period of sustained pressure from Alcorcon, but broke clear and almost doubled their lead on 77 minutes through Ighalo, who could only hit the side-netting.
Three minutes later, Ighalo did make it 2-0, showing some fantastic skill to get past the defenders before finishing well.