Sevilla into top 10
Sevilla's Gary Medel
The Andalusia club are up to 32 points from 24 matches and leapfrogged Real Valladolid. Deportivo remain rooted to the bottom of the standings and looked destined for relegation to the second tier.
Sevilla started the match like a house on fire and opened the scoring in the sixth minute through Ivan Rakitic, who benefitted from a good assist by Coke.
The hosts made it 2-0 on 27 minutes, with Gary Medel converting a cross from Jesus Navas to put daylight between themselves and the strugglers.
However, Deportivo gave themselves some hope when Riki found the back of the net five minutes later via Sevilla midfielder Geoffrey Kondogbia, who could yet be credited with an own goal.
But any hopes they had of a comeback were quickly extinguished by Medel, who notched up his second goal of the night on 40 minutes to ensure Sevilla headed into the half time break with a solid 3-1 advantage.
They took their foot off the pedal in the second half but easily held Deportivo at bay, picking up a much-needed victory to boost their hopes of a top-half finish.