The result meant Real moved up to third place, one point ahead of Valencia and three behind leaders Barcelona.
Joaquin, 37, became the oldest scorer in a Seville top-flight derby when he rose to head home at the near post in the 79th minute, shortly after the visitors had had midfielder Roque Mesa sent off for two bookings.
Atletico Madrid striker Radamel Falcao scored two superb goals and Diego added a late third to seal a commanding 3-0 victory over Athletic Bilbao in the all-Spanish Europa League final on Wednesday.
Cristiano Ronaldo struck midway through the first half as leaders Real Madrid won 1-0 at Malaga in La Liga on Saturday, while Atletico Madrid stayed hot on their heels after Diego Costa netted in a 1-0 victory over Espanyol.
With Real Madrid facing an injury crisis ahead of Wednesday's Champions League clash with Atletico Madrid attention will be on talisman Cristiano Ronaldo to lead them through but James Rodriguez may hold the key.
Antoine Griezmann scored twice off the bench as Atletico Madrid sealed a place in the King's Cup quarter-finals with a 3-0 win at home to Rayo Vallecano on Thursday while Valencia also advanced with victory by the same scoreline at Granada.
Sevilla claimed their second King's Cup triumph in four years when Diego Capel's early strike and a late breakaway goal from Jesus Navas fired them to a 2-0 win over Atletico Madrid on Wednesday.
Atletico Madrid's La Liga title challenge took a nosedive when they slumped to a shock 3-0 defeat at Osasuna on Sunday, leaving Real Madrid three points clear at the top.
Joao Miranda and new signing Mario Mandzukic led Atletico Madrid to a 2-1 home win in La Liga on Saturday as visitors Eibar were unable to cope with the aerial threat of the champions.
Atletico Madrid striker Mario Mandzukic's early goal secured a 1-0 win over Real Madrid and a 2-1 aggregate success to clinch the Spanish Super Cup and gain some revenge for last season's Champions League final defeat.
IMAGES from the Champions League matches played on Tuesday.
The 22-year-old Spain striker has ruled out a move away from Atletico Madrid.
Atletico celebrate anniversary with 3-1 comeback win over Mallorca
Simeone's side leapfrogged Real Sociedad into fourth on 42 points, while Sevilla stayed third in the standings on 46 after beating Las Palmas 1-0, also on Sunday, thanks to a late strike from substitute Joaquin Correa
Christmas came early to the 'City of Joy' as the inaugural Indian Super League champions Atletico de Kolkata returned home to a hero's welcome.
A quickfire Arda Turan double, including an acrobatic bicycle kick, fired Atletico Madrid to a 3-1 home win over Espanyol in La Liga on Sunday and lifted the Europa League semi-finalists up to seventh.
Barcelona and Atletico Madrid dropped their first points of the season on Saturday, missing the chance to equal the record for the best-ever La Liga start.
Real Madrid's stuttering run continued as they were held 1-1 at home by La Liga minnows Eibar on Sunday, drawing a fourth consecutive game in all competitions for the first time in more than a decade.
Photos from the UEFA Champions League last 16 first leg-matches played on Wednesday
Atletico Madrid surrendered top spot in La Liga to Barcelona when they were held to a 0-0 draw at home to 10-man Sevilla in a fiercely contested La Liga clash on Sunday.
A repeat of the 2014 Champions League final between Real Madrid and Atletico Madrid is still possible after Friday's semi-final draw.
Atletico Madrid kept pace with leaders Barcelona and restored their five-point lead over third-placed city rivals Real when Diego Costa and David Villa each scored a penalty in a 2-1 win at Granada in La Liga on Thursday.
Atletico Madrid right back Juanfran has thanked fans for the support he received following his penalty shootout miss in Saturday's Champions League final defeat by Real Madrid. The defender's effort rebounded off the post before Cristiano Ronaldo scored the winning spot kick to hand Real their 11th European Cup in Milan. Spain international Juanfran was in tears and did not speak to the media after the match but on Monday he wrote a letter on the club's official website. "I will never forget your displays of affection when I came to ask for your forgiveness," he said. "Seeing my tears reflected in the faces of the thousands of Atleticos that packed that end of the stadium helped me cope with the tremendous sadness I felt in those hard times."
Atletico Madrid got their La Liga campaign up and running in less than convincing fashion when Antoine Griezmann's deflected free kick secured an edgy 1-0 win at home to promoted Las Palmas on Saturday.
Barca looked set for a third consecutive league draw as they created scant opportunities but they were presented with the advantage of an extra man when Villarreal midfielder Daniel Raba was given a straight red card for a wild, studs-up challenge on Sergio Busquets on the hour mark.
News of all that's transpired on and off the football field
News of all that's transpired on and off the football field
Atletico Madrid have agreed to sign Colombia striker Radamel Falcao from Porto for a fee of 40 million euros ($57.26 million).
Atletico Madrid will face holders Real Madrid in the last 16 of the King's Cup after a double from Mario Mandzukic sealed a 5-2 aggregate victory over lower league Hospitalet on Thursday.
Real Madrid's early-season woes deepened when they lost 2-1 at home to La Liga champions Atletico Madrid, while substitute Neymar struck twice in Barcelona's 2-0 win against visiting Athletic Bilbao on Saturday.
Three consecutive defeats by direct rivals in the Primera Liga has left Atletico Madrid coach Javier Aguirre under pressure to get a good result against Liverpool at home in the Champions League.
Barcelona had to come from a goal down to rescue a 1-1 draw at mid-table Levante on Sunday, leaving Atletico Madrid with a chance to go top of La Liga.
Atletico should have plenty of money available after talismanic striker Antoine Griezmann said last month he is to leave the club.
A stoppage time header by fullback Lucas Vazquez earned 10-man Real Madrid a 1-0 victory at lowly Alaves.
Leaders Barcelona played out a second straight 0-0 draw in LaLiga after mid-table Getafe battled for a home point in a hard-fought game on Sunday.
Midfielder Koke issued a rallying cry to his Atletico Madrid teammates on Saturday ahead of next week's Champions League final against Real Madrid.
Atletico Madrid set up a King's Cup final with city rivals Real after Diego Costa and Radamel Falcao scored in a 2-2 second leg draw at Sevilla on Wednesday, to progress 4-3 on aggregate.
Atletico Madrid have little time to celebrate their stunning La Liga triumph and must immediately turn their focus on Saturday's Champions League final against city rivals Real Madrid.