Coke broke the deadlock midway through the first half before a red card to Stefan Babovic complicated things for the visitors, and the hosts romped to victory in the second period thanks to further goals by Coke, Jose Antonio Reyes and Alvaro Negredo.
Unai Emery's side started the far stronger with Geoffrey Kondogbia, Negredo and Ivan Rakitic all missing decent chances to score early on.
It was little surprise when the opening goal did arrive, on 27 minutes.
Sevilla won a free-kick on the left side of the opposition area, which was taken by Rakitic. The Croatian delivered a low ball towards Negredo, who back-heeled it across the penalty area where full-back Coke rifled it into the net.
Zaragoza were struggling to get into the game and their plight was significantly worsened just three minutes after the goal, when Babovic was given his second yellow card of the game for pulling Kondogbia to the ground, leaving his team with 10 men for the remaining hour of the match.
Goalkeeper Leo Franco did well to stop a powerful shot from Reyes before the break and Zaragoza went into the dressing room at half-time with still a glimmer of hope of getting something from the game.
However, any feelings of optimism they may have had were soon killed off when Coke doubled his tally. The defender picked the ball up on the right wing about 25 yards from goal and lashed the ball far into the top corner.
Ten minutes later Sevilla launched a counter attack, Reyes combining well with Jesus Navas and the former Arsenal player beat Leo Franco with ease with a left-footed drive.
Top scorer Negredo soon joined in on the act, sliding home a perfect pass by Reyes to cap off a horrible homecoming for former Sevilla coach Manolo Jimenez, whose side are still yet to win in 2013 and remain two points above the relegation zone.