It seemed the 2009/10 champions would have to settle for a draw when Federico Fazio’s fourth-minute strike was cancelled out by Cristian Lopez after 69 minutes.
But Juan Cala put Sevilla ahead seven minutes from time and Alvaro Negredo added a last-gasp spot-kick – after Ernesto Galan had been sent off – to give the hosts a further cushion ahead of the second leg.
Last season’s finalists Athletic Bilbao began this year’s campaign with a goalless draw at third tier Eibar.
Bilbao, beaten by Barcelona in the showpiece match in May, have struggled to match the impressive form that also saw them reach the final of the UEFA Europa League last season and their misery continued tonight.
Alberto Bueno’s first-half goal gave 10-man Valladolid a slight 1-0 advantage over Primera Division rivals Real Betis.
The 24-year-old broke the deadlock six minutes before the interval, and although second-half substitute Henrique Sereno was dismissed in the 65th minute, Valladolid held on.
Pedro Geromel’s 71st-minute leveller gave Real Mallorca a precious 1-1 draw at Deportivo La Coruna.
Manuel Pablo put the hosts ahead nine minutes after half-time but Geromel gave Mallorca the advantage heading into the second leg.
Fernando Velasco’s 38th-minute penalty gave Segunda Division B outfit Melilla a shock 1-0 win over Levante, who are currently sixth in the Primera Division.
After taking the lead, Carlos David’s 70th-minute sending off left Melilla hanging on, which they did with aplomb.
Segunda Division sides Sporting Gijon and Cordoba were also surprise victors as they defeated top-flight teams Osasuna and Real Sociedad respectively.
Javier Patino (43) and his replacement Vincenzo Rennella (75) gave Cordoba a 2-0 win, while Gaston Sangoy’s 15th-minute strike gave Gijon a surprise 1-0 triumph.
Jaime Gavilan scored twice as Getafe thumped Ponferradina 4-0. Gavilan scored in the 13th and 65 minutes – in-between Pablo Sarabia’s strike on half-time – while Paco Alcacer sealed the rout five minutes later.