Another double from Deportivo's Oriol Riera could not prevent Sevilla from picking up their first win in three league games, which cements their fifth place in the table on 49 points.
Riera opened the scoring in the 28th minute only for Vitolo to quickly respond with an equaliser.
The Sevilla striker then demonstrated more clinical finishing after 52 minutes, having been allowed space in the centre of the penalty area.
Kevin Gameiro converted a controversial penalty after Vitolo, played onside by injured defender Juanfran, was felled by Pablo Insua in the box.
Riera pulled a goal back for Deportivo before the Brazilian central defender Sidnei diverted a Vitolo shot into his own net.
As the conclusion to a contest featuring some hapless defending, Sevilla defender Nicolas Pareja upended Helder Costa for another penalty, which Deportivo's Lucas Perez struck home.
Later, leaders Real Madrid face Athletic Bilbao with the chance to extend their lead to five points with second-placed Barcelona at home to Rayo Vallecano on Sunday.
(Writing by Tim Hanlon; Editing by Ian Chadband)
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