Robert Lewandowski got off the mark for Barcelona with a double as Ansu Fati starred as a substitute in a 4-1 victory over Real Sociedad on Sunday, while Villarreal won at Atletico Madrid.
Poland striker Lewandowski, celebrating his 34th birthday, put Barca ahead inside 50 seconds before Alexander Isak levelled for La Real in San Sebastian.
But Fati came off the bench to create goals for Ousmane Dembele and Lewandowski, before completing the scoring himself.
Barca's first win of the season followed a disappointing goalless draw at home to Rayo Vallecano on the opening weekend.
Coach Xavi had called for "patience" from supporters after a summer spending spree which saw Lewandowski, Raphinha, Andreas Christensen and Franck Kessie all move to the Camp Nou.
That quartet all made their debuts against Rayo, but France defender Jules Kounde is still to be registered by the club after his transfer from Sevilla as they look to overcome financial problems.
The visitors made a dream start on Sunday, though, as 18-year-old full-back Alejandro Balde raced clear and sent in a low cross which was tapped home by Lewandowski.
He scored 344 goals during a trophy-laden eight-year spell at Bayern Munich before leaving for 45 million euros in July.
But the home side hit back in the sixth minute, as Frenkie de Jong lost the ball in midfield and Isak raced clear before lofting the ball into the net.
Sociedad were proving a tough nut to crack for Barca, but the game changed when Fati was sent on in the 64th minute.
The 19-year-old's brilliant backheel teed up Dembele to drill a left-footed strike into the bottom corner just two minutes later, before another clever touch found Lewandowski to score.
Fati, who endured two injury-plagued seasons after breaking into the first team in 2019/20, got a goal himself late on as he collected Lewandowski's volleyed flick and slotted in.
Earlier, Villarreal moved to the top of the fledgling table as second-half goals from Yeremy Pino and Gerard Moreno secured a 2-0 victory at Atletico.
Unai Emery's men opened their season with an impressive 3-0 win at Real Valladolid last weekend but the scalp of Atletico will raise hopes of a possible challenge for Champions League qualification.
The result was a reality check for the capital side, though, who had also started the campaign with a 3-0 success at Getafe.
Villarreal, who reached last season's Champions League semi-finals, are one of four teams with two wins from two matches and edged above reigning champions Real Madrid on goal difference.
The away side made a fast start at the Estadio Metropolitano, with Atletico goalkeeper Jan Oblak forced into fine saves from Giovani Lo Celso and Etienne Capoue.
Moreno thought he had given Villarreal a half-time lead, but his effort was ruled out for a handball.
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