Deportivo did have one back moments later through Riki, but Medel added his second of the evening five minutes before the break to make it 3-1 at the interval.
The away side improved in the second period, but they could not find a way back into the match as Sevilla picked up the three points.
Read how it all unfolded in Sports Mole's minute-by-minute live commentary of the action below.
SEVILLA: Beto; Spahic, Fazio, Coke, Moreno; Reyes, Rakitic, Medel, Kondogbia, Navas; Negredo
DEPORTIVO: Arazubia; Ze Castro, Evaldo, Kaka, Silvio; Aguilar, Assuncao, Bergantinos, Riki; Gama, Pizzi