Sergio Ramos deflected Lamine Yamal's header into his own net in the 76th minute to break the deadlock in a tight clash.
Youngster Fermin Lopez rescued Barcelona a 2-2 draw at Real Mallorca on Tuesday which extended his team's La Liga lead, even though the champions dropped two points.
Barcelona coach Xavi Hernandez praised his side's "winning character" after a sensational 3-2 comeback to beat Celta Vigo on Saturday and move top of La Liga, ahead of Monday's Madrid derby.
Felix shone for the Spanish champions on a stroll on a warm night in the Catalan capital, helped on their way by an own goal, with Robert Lewandowski and Gavi also scoring.
Manchester City begin their defence of the Champions League on Tuesday when the group stage kicks off in the last season in its current format as Europe's elite club competition gets ready for a radical change.
The emphatic victory places Barcelona provisionally top of the table, a point clear of rivals Real Madrid who host Real Sociedad on Sunday.
Yamal became Barcelona's youngest debutant at 15 years and 290 days old against Betis in April last season.
Barcelona took the lead through Jules Kounde's header in the first half but Chimy Avila drilled the hosts level with less than 15 minutes remaining.
Manchester City headline Pot A featuring Barcelona, Bayern Munich, Napoli, Paris Saint-Germain, Feyenoord, Sevilla and Benfica.
After several near misses in recent years, Pep Guardiola's side won the trophy for the first time when they defeated Inter Milan 1-0 in last season's final in Istanbul in June.
Barcelona starlet Lamine Yamal shone in a thrilling 4-3 win for the Spanish champions at Villarreal on Sunday in La Liga
Barcelona were held to a frustrating goalless draw in the opening week by Getafe, then Pedri Gonzalez only breaking the deadlock as the clock ticked down against Cadiz.
Pedri and Ferran Torres' late strikes earned La Liga champions Barcelona a 2-0 win over Cadiz in their first competitive home game away from Camp Nou on Sunday.
Barcelona coach Xavi Hernandez will serve a two-match suspension after being sent off in his team's La Liga season opener against Getafe
Barcelona on Wednesday announced that former player Deco was taking over as sporting director.
Spanish champions Barcelona began their La Liga title defence with a frustrating 0-0 draw at Getafe on Sunday, with both sides reduced to 10 men in a bad-tempered clash
Neymar is "probably leaving" Paris Saint-Germain, with an offer from Saudi Arabia said to be on the table.
As Kylian Mbappe's contract dispute with Paris Saint-Germain rumbles on, the Qatari-backed club announced a new signing - Ousmane Dembele on a five-year-deal from Barcelona