Athletic Bilbao stunned Real Madrid 1-0 at San Mames to hand Barcelona a chance of claiming top spot in La Liga by the end of the weekend, while in La Coruna, the visitors triumphed 4-3 in a match that involved two penalties and an own goal.
The victory saw Sevilla strengthen their hold on fifth position, which comes with a UEFA Europa League berth, as they rose to 49 points, four clear of sixth-placed Villarreal, who play on Sunday.
Deportivo opened the scoring in the 28th minute with Oriol Riera poking Ivan Cavaleiro's low cross inside the near post but Vitolo equalised five minutes later after a smart one-two with Carlos Bacca.
A flowing move in the 52nd minute saw Sevilla grab the lead, as Aleix Vidal's cut-back picked out Vitolo's late run into the box and the 25-year-old midfielder cracked a first-time shot past Deportivo goalkeeper Fabricio.
Pablo Insua's late tackle on Vitolo handed the visitors a chance for a third goal, and Kevin Gameiro made no mistake from the spot in the 65th minute.
But just as Sevilla appeared to be in control, Riera notched his own brace for the hosts, volleying Luisinho's cross home from close range with 18 minutes remaining.
An 83-minute own goal by Sidnei from Vitolo's cross reinstated Sevilla's two-goal cushion and although Lucas Perez converted a penalty for Deportivo in stoppage-time, the visitors held on for victory.
In Bilbao, Aritz Aduriz's powerful header in the 26th minute clinched three points for the home side, who have won three games in a row in all competitions.
It continued Real's inconsistent form in La Liga with Carlo Ancelotti's men having won just two of their past five matches.
The capital club have 61 points at the top of the standings but Barcelona (59) could leapfrog Real with a win over Rayo Vallecano on Sunday, while third-placed Atletico Madrid (54) will also be looking to take advantage against Valencia.
At the other end of the table, Granada claimed their first win in five games, accounting for Malaga 1-0.
Granada sit second-bottom but the victory took them to 22 points, three clear of safety.
In Saturday's other match, Elche defeated Almeria 1-0.
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