The match was effectively ended as a contest after 26 minutes when referee Carlos Delgado sent off Jaen's Daniel Torres for handball and gave Atletico the chance to open the scoring from the penalty spot.
Los Rojiblancos took full advantage of the extra man and further strikes from Adrian and Raul Garcia gives them a seemingly unasailable lead in the two legged tie.
Atletico started brightly at the Nuevo Estadio de la Victoria and should have been in front inside three minutes.
Raul Garcia found space down the right hand sign and delivered an inviting ball into the area but Koke could only put his header straight into the arms of goalkeeper Toni Garcia.
Atletico continued to dominate possession in the opening stages but los rojiblancos struggled to create clear cut chances against a robust Jaen defence.
Real Jaen, backed by a record crowd of 18,000, began to feel their way into the game after a nervy opening period and they almost opened the scoring after 16 minutes.
Jerez floated a deep cross into the box that fell of the feet of Santi Villa at the back post. The winger checked back onto his right foot and fired in a low shot that needed a goaline block from Cata Diaz with Courtois beaten.
Clear cut chances were proving difficult to come by and Atletico’s Cristiano Rodriguez resorted to the spectacular, taking a clearance on the chest and volleying goalwards, and over, from 25 yards out.
Jaen continued to pose a threat to Atletico at the other end and it took a smart stop from Courtois to keep out Jerez’s effort from the edge of the area, the Belgian diving full length to tip the ball away from goal.
The match’s turning point arrived after 26 minutes. Atletico once again exploited Jaen down the right flank and though Garcia was able to keep out Rodriguez’s initial effort, defender Daniel Torres was adjudged to have blocked Diego Costa’s follow up with his arm.
Torres, who was on the ground when the ball struck him, was shown a red card by referee Carlos Delgado and Diego Costa sent Garcia the wrong way from the spot to put Madrid in the most commanding of positions.
A dejected Jaen managed to hold out until have time, although it took a timely challenge from Servando Sanchez to stop Costa from doubling Atletico’s and his own tally for the evening.
The hosts started the second half with renewed vigour, managing to sustain a prolonged period of pressure on the Atletico goal but struggling to carve out any telling opportunity.
They were made to pay for this when Los Rojiblancos lodged the most clinical of counterattacks.
Madrid broke through the middle and the ball was slipped wide to substitute Adrian who cut inside into the box and poked home past Garcia to give his side breathing space.
Jaen began to show signs of frustration in the closing period and Jerez was lucky to stay no the pitch when his studs left their mark on Cristiano Rodriguez.
Atletico came close to adding a third near the end when substitute Oliver got his head on Silvio’s cross but the Atletico B forward was denied by the legs of Garcia.
Garcia then pulled off a sensational double save to deny Costa and Adrian but couldn’t do anything to deny Raul Garcia from adding a third late in stoppage time.
Atletico now take a commanding first leg lead back to the Vicente Calderon and will be confident of securing a safe passage into the fifth round of the Copa del Rey.