An own goal by Carlos Marchena in the final minute of the first half gave the visitors the lead, with Ighalo doubling their advantage shortly after the interval.
Depor then missed a number of chances to get themselves back into the game and their night was summed up when they conceded a dubious penalty in the last minute and saw Manuel Pablo sent off, with Guilherme Siqueira converting from the spot.
The first half was evenly matched with both sides having several chances to take the lead.
But Deportivo's nerves were evident when Paulo Assuncao played a poor backpass towards his goalkeeper Daniel Aranzubia, which was intercepted by Carlos Aranda, who fired wide from 40 yards out to the relief of the Depor fans.
With a minute to go in the first half Deportivo forward Riki missed a glorious chance after reacting too slowly to a cross by Diogo Salomao.
Barely a minute later the Galicians, who should have gone into the break ahead, were picking the ball out of their own net.
Aranda's cross was headed against the far post by Nolito and the ball bounced out and ricocheted off the unfortunate Marchena and trickled into the net.
There was nothing fortunate, however, about Granada's second goal, which came in the 50th minute.
Siqueira and Ighalo exchanged a one-two on the edge of the area and the former squared the ball back to the latter, who fired past Aranzubia.
Deportivo did not give up after the second goal, but their finishing let them down.
Ighalo missed a chance to grab his second goal of the night in the last minute when he saw his shot tipped over by Aranzubia, but there was still time for Deportivo's night to get even worse.
Ighalo took a tumble in the box in injury time after a challenge by Manuel Pablo and was awarded a penalty.
The full-back took his anger out on the referee, who showed him a straight red card for dissent, and then Siqueira stepped up to fire the penalty into the top corner.