Goalkeeper Andres Palop emerged as Sevilla's hero by saving three penalties in the shootout to give his side victory over Espanyol.
A 5-1 victory enabled them retain the top spot in the Primera Liga.
Higuain had a disappointing Copa America tournament in July, scoring two goals during the competition and missing his spot kick as Argentina lost on penalties to Chile in the final.
Jose Mourinho was delighted that Chelsea made a winning start to their Champions League campaign on Wednesday, but said he was not happy that Manchester United, Manchester City and Arsenal had all lost their opening matches.
Manchester City embark on a fifth Champions League campaign buoyant after a perfect start to their domestic season but still searching for the secret formula against Europe's top brass.
The win lifted Hamburg, who needed a relegation playoff to stay up last season, to seventh on six points.
images from the UEFA Champions League matches played across Europe on Wednesday
Holders Barcelona produced a second-half blitz to come from behind and beat Athletic Bilbao 3-1 to book a place in the King's Cup semi-finals after Atletico Madrid crashed out in a shock 3-2 defeat by Celta Vigo.
West Bromwich Albion have bolstered their defensive ranks by signing centre half Jonny Evans from Manchester United on a four-year deal.
New strikers Carlos Bacca and Luiz Adriano bagged their maiden Serie A goals to give AC Milan their first points of the season with a 2-1 home win over Empoli on Saturday.
Holders FC Barcelona have been placed in Group E, along with Bayer Leverkusen, AS Roma, Dinamo Zagreb.
The defending champions suffered an extraordinary 4-1 away defeat in the Spanish League.\n\n
Champions Barcelona begin their bid for a sixth La Liga title in eight years at Athletic Bilbao on Sunday knowing that fellow heavyweights Real Madrid could, unusually, be just one of several challengers for their crown.
Second division Mirandes caused an upset by knocking Deportivo La Coruna out of the King's Cup on Tuesday and Sevilla joined them in the quarter-finals after making light work of city rivals Real Betis.
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Aritz Aduriz's second half hat-trick sent Barcelona spinning to a shock 4-0 defeat at Athletic Bilbao in the first leg of the Spanish Super Cup on Friday.
Winning the treble last season has spurred Barcelona to try and win all six trophies up for grabs this year and replicate the feat they achieved in 2009, midfielder Andres Iniesta said on Monday.
Images from Champions League matches played across Europe on Tuesday
Barcelona will be missing the lethal touch of Neymar in attack for the UEFA Super Cup against Sevilla.
Neymar and Lionel Messi grabbed a goal each in the first half as Barcelona rolled over Roma 3-0 in the traditional Gamper Trophy pre-season match on Wednesday.
Manchester City's all-conquering season reached new peaks as Sergio Aguero became the club's all-time top scorer with a decisive goal in a thrilling 4-2 victory at Napoli that put them into the Champions League last 16 on Wednesday.
Cristiano Ronaldo ensured Atletico Madrid fans will have bitter memories of the last local derby at the Vicente Calderon stadium by scoring a hat-trick in a 3-0 win for La Liga leaders Real Madrid on Saturday. Ronaldo's deflected free kick put Real in charge in the 23rd minute in the first meeting of the teams since the Champions League final in May. The prolific Portuguese killed off Atletico's resistance by winning and converting a penalty in the 71st minute and capped a harrowing night for the home side by tapping in the third in the 77th.
Defender Filipe Luis has rejoined Atletico Madrid from Chelsea in a reported 16 million euro ($17.66 million) deal, the Spanish club said.
Barcelona closed in on the La Liga title by thrashing local rivals Espanyol 5-0 on Sunday as Atletico Madrid dropped out of the race after losing 2-1 at Levante and Real Madrid beat Valencia 3-2.
New Valencia coach Gary Neville remains without a La Liga win after his side twice recovered from a goal down to rescue a fortunate 2-2 draw at home to Getafe on Saturday.
Barcelona have completed their business in the latest transfer window and the Spanish and European champions' squad is now "closed", president Josep Bartomeu said on Thursday.
Barcelona coach Luis Enrique was pleased they got straight back into their stride with Tuesday's 2-1 friendly win over the Los Angeles Galaxy.
Mateo Kovacic's late strike avoided embarrassment for Real Madrid as the European champions surrendered a two-goal lead before drawing 3-3 with Legia Warsaw in an enthralling Champions League game played amid an empty stadium on Wednesday.
Barcelona's new midfield playmaker Arda Turan has said it will be tough for him not being able to play until January due to a ban on the club on registering players.
A red hot Luis Suarez scored four goals and contributed three assists as Barcelona's stuttering La Liga title charge sparked back to life with a spectacular 8-0 thrashing of Deportivo La Coruna on Wednesday.
Barcelona's stuttering title bid suffered another setback when they lost 2-1 at home to Valencia on Sunday, while Atletico Madrid moved level on points with the La Liga leaders after a comfortable win over Granda.
The Millennium Stadium in Cardiff will host the 2017 Champions League final, UEFA general secretary Gianni Infantino said on Tuesday. The Friends Arena in Stockholm will be the venue for the 2017 Europa League final.
Everton have signed winger Gerard Deulofeu from Barcelona on a three-year contract for six million euros ($6.7 million), the Premier League club said on Thursday.
A summary of Tuesday's group matches in the UEFA Champions League.
Barcelona defender Dani Alves has agreed a two-year contract extension to the end of the 2016-17 season with an option for a further year, the Spanish and European champions said on Tuesday.
His season has been 10 out of 10 and there is no reason to break the contract, says Josep Maria Bartomeu.
An impudent individual goal from Philippe Coutinho steered Liverpool comfortably into the quarter-finals of the Europa League on Thursday after a 1-1 draw at bitter rivals Manchester United completed a 3-1 aggregate win.
'Will I be playing at Barca next season? It's an unknown'