Chelsea showed off its new-found attacking sparkle in a 6-3 win over Everton on the day Manchester City lost its cutting edge to slip to a surprise first defeat in its Premier League title defense.
City's 1-0 home loss to Stoke on Saturday was exacerbated by its title rival's wild victory at Goodison Park, in which Spain striker Diego Costa scored in the first and last minutes to continue the superb start to his Chelsea career.
Another big-money arrival in English football, Angel Di Maria, made a promising debut for Manchester United but its 0-0 draw at promoted Burnley left Louis van Gaal's side with just two points from three games - despite a spending spree of 130 million pounds ($215 million) this summer.
Chelsea has no such problems, with a third straight win leaving the team top of the early standings on goal difference from surprising Swansea.
On a day to forget for Everton and United States goalkeeper Tim Howard, Costa scored after just 34 seconds and Branislav Ivanovic put Chelsea 2-0 ahead inside three minutes, only for Kevin Mirallas to reduce the deficit for Everton just before halftime.
Seamus Coleman's own goal in the 66th minute sparked a rush of five goals in a chaotic 11-minute spell during which both defenses were carved open to the dismay of the team's managers.
Steven Naismith made it 3-2, Nemanja Matic regained Chelsea's two-goal lead in the 74th but Everton came back again through Samuel Eto'o's header on his debut, against the club that released him in the summer. Ramires put Chelsea 5-3 ahead and Costa wrapped up a madcap second half with a low finish after a back-heel from substitute Didier Drogba.
Swansea is tied on nine points with Chelsea after beating West Bromwich Albion 3-0 thanks to two goals from Nathan Dyer and another from Wayne Routledge.
Also Saturday, Crystal Palace drew 3-3 at Newcastle, Southampton won 3-1 at West Ham and Queens Park Rangers beat Sunderland 1-0.
Atletico Madrid held on to beat Eibar 2-1 on Saturday to record an unconvincing first win of the Spanish league season.
Atletico received the trophy as champions of last season before the match to the delight of the packed Vicente Calderon Stadium. And it looked ready to keep the celebration going after taking a 2-0 lead in a one-sided half hour following headed goals by Miranda and Mario Mandzukic in the 11th and 25th minutes.
But Eibar defender Abraham Minero's goal in the 33rd gave the promoted club renewed confidence, and the modest Basque side kept alive its chances to draw through a second half that had the home fans on edge.
Also, Athletic Bilbao routed Levante 3-0 while Celta Vigo settled for a 1-1 draw at Cordoba.
Schalke captain Benedikt Hoewedes equalized to give his side a 1-1 draw against Bayern Munich in the Bundesliga on Saturday, denying Xabi Alonso a win on his debut for the German champions.
Hoewedes bundled the ball over the line in the 62nd minute as Alonso's desperate attempt to clear came back off the World Cup winner's left arm.
Robert Lewandowski opened the scoring in the 10th after carving open the Schalke defense.
Bayer Leverkusen twice came from behind to defeat Hertha Berlin 4-2 and maintain its winning start, while newly promoted Paderborn beat Hamburger SV for its first ever win in the Bundesliga.
Wolfsburg drew with Eintracht Frankfurt 2-2, Werder Bremen drew 1-1 with Hoffenheim and Cologne won 2-0 at Stuttgart.
New Juventus coach Massimiliano Allegri kicked off his time in charge with a victory as his team won 1-0 at Chievo Verona in the Serie A opener on Saturday.
Juventus showed that little has changed from the spirit which drove it to three consecutive league titles as Martin Caceres helped open the scoring in the sixth minute.
Caceres headed Carlos Tevez's corner toward goal, although it eventually went in off the back of Cristiano Biraghi.
Juventus had several chances to extend its advantage and hit the woodwork three times in the first half.
Roma, last year's runner-up, won 2-0 at home to Fiorentina, with Radja Nainggolan and Gervinho scoring.
Monaco striker Dimitar Berbatov salvaged a 1-1 draw with Lille in the French league on Saturday after Radamel Falcao was left out of the squad amid speculation about his future.
Lille striker Nolan Roux opened the scoring with a half-volley in the 18th minute, but Berbatov equalized from close range in the 61st.
Falcao watched the game from the stands in a black suit, white shirt and red tie. The Colombia striker scored the lone goal in the 1-0 victory over Nantes last weekend but has been linked with a move to Real Madrid, Manchester City or Juventus in the final days of the transfer window.
Lille has eight points from the first four games, four more than Monaco.