French forward Wissam Ben Yedder put Sevilla in front in the 26th minute after racing in behind Ramos while Miguel Layun doubled the home side's lead on the stroke of halftime, knocking into an empty net from close range.
Former Sevilla defender Ramos struck the crossbar from the spot in the 58th minute and then put through his own net to stretch the home side's advantage to three goals in the 84th as he tried to cut out a cross from Gabriel Mercado.
Zidane made eight changes to his side after Sunday's grueling 2-2 draw at arch rivals Barcelona, only retaining Ramos, French striker Karim Benzema and midfielder Casemiro.
Toni Kroos, Luka Modric, Marcelo and top scorer Cristiano Ronaldo all remained in the Spanish capital to stay fresh for the Champions League final against Liverpool in Kiev on May 26.
Champions Barcelona stretched their heavy lead over Atletico to 15 points after thrashing Villarreal 5-1 at home on Wednesday.
They climbed two points above Getafe into seventh place, the final Europa League qualification spot, with two games left of the campaign.