The visitors claimed the better of the attacking possession in the first period and took the lead right on the stroke of half time.
Deportivo defender Marchena put through his own net moments after Nolito headed against the crossbar from Carlos Aranda's cross.
Granada doubled their advantage six minutes into the second half when Ighalo rifled Guillherme Siqueira's cut-back into the bottom corner.
The hosts had their chances to reduce the deficit in the second period - with Riki and Nelson Olivera almost finding a way through - and Ighalo shot inches wide at the other end in the 71st minute.
Granada keeper Tono was called into action four minutes later, producing an impressive stop to deny Pizzi and ensure his side ended the match with a clean sheet.
Deportivo's evening ended on a sour note when Manuel Pablo was sent off for arguing with the referee after he had brought down Ighalo in the area. Siqueira dispatched the resultant spot-kick in the final minute to make it three for the visitors.