Alvaro Negredo opened the scoring for the visitors 39 minutes after being played in by Jose Antonio Reyes.
Negredo then turned provider after the interval, crossing for Del Moral's first early in the second half.
And Del Moral added gloss tot he result with a strike deep into injury time.
Sevilla move to within four points of sixth place, the final Europa League qualifying spot, while local rivals Granada stay six points clear of the relegation zone despite the loss.
