Reborn French international striker Karim Benzema scored the decisive goal on 15 minutes to make it a happy 48th birthday for Mourinho and give Sevilla, who were furious at not being awarded a goal when the ball appeared to cross the line, an uphill task to reach the final for the second successive season.
Mourinho had been given an early birthday present with Togo international striker Emmanuel Adebayor snapped up on loan from Manchester City to bolster his striking options, but Benzema showed he would not surrender his place without a fight.
With a quarter of an hour gone a neat interchange of passes released Benzema, who dribbled past one man before cutting inside to curl a left-footed shot into the corner.
Benzema had scored the winner in Sunday's 1-0 home win over Real Mallorca and was congratulated with a high five from Mourinho on the touchline.
Madrid were on top for most of the first half but on the chime of half-time Sevilla were convinced they had equalised.
Luis Fabiano, who scored a hat-trick against Levante at the weekend, went around Iker Casillas and fired the ball goal bound, but Raul Albiol got back to clear off the goal line although all the Sevilla players were adamant the ball had crossed the line.
The referee and his assistant did not agree and Sevilla players went off complaining at the half-time interval.
Madrid were the better side after the break with Xabi Alonso going close and the visitors missed a glorious chance to get a second away goal on 79 minutes when Cristiano Ronaldo and Mesut Ozil were both denied by some last ditch defending.
The match finished with Real goalkeeper Casillas holding his head after appearing to get struck by an object from the crowd as tempers boiled over.
Real now have the edge in the tie as they bid to win the competition for the first time since 1993, while holders Sevilla will need to come back and score in the second leg at the Santiago Bernabeu.
Barcelona, record winners of this competition lifting it 25 times, host Almeria in the first leg of the other semi-final at Camp Nou later on Wednesday.
Almeria have reached the last four for the first time in their history but are underdogs against a Barcelona side that thrashed them 8-0 in the league this season.