Scoring for the second straight game, Diego Costa set Chelsea on its way to a 2-0 home victory over Leicester to join Swansea with back-to-back wins after two rounds.
The Spanish league got underway with Malaga's eventful win over Athletic Bilbao and the German league was treated to its quickest goal ever.
Here is the best of the action from Europe's top leagues:
Diego Costa kept up the prolific start to his Chelsea career, scoring his team's first goal in the second half in the 2-0 win over Leicester.
The Spain striker scored on his Chelsea debut in a 3-1 win over Burnley on Monday and netted again five days later, breaking down Leicester's stubborn resistance at Stamford Bridge in the 63rd minute.
Belgium winger Eden Hazard's solo effort in the 77th ensured Chelsea has maximum points after two games against teams promoted from the second-tier League Championship. Didier Drogba was given a standing ovation when he came on as a second-half substitute for Costa for his first home match in his second spell at Chelsea.
Swansea is the only other side with back-to-back wins so far after beating Burnley 1-0, while Arsenal has four points after getting goals from Aaron Ramsey and Olivier Giroud in the final seven minutes to recover for a 2-2 draw at Everton.
West Ham won 3-1 at Crystal Palace while the games between Aston Villa-Newcastle and Southampton-West Bromwich Albion finished 0-0.
Malaga held on to beat Athletic Bilbao 1-0 to kick off the Spanish league on Saturday and give new coach Javi Gracia a winning debut at La Rosaleda Stadium, although the game was marred by two red cards in the final minutes.
Malaga scored in the 34th minute when Luis Alberto converted the rebound from his own missed penalty after goalkeeper Gorka Iraizoz blocked his spot kick.
Tempers flared near the end, when Malaga lost two players with direct red cards. Sergio ''Duda'' Barbosa was first sent off for shoving Bilbao's Iker Muniain to the turf in the 88th, and Vitorino Antunes compounded that error by earning his exit with a dangerous tackle to cut down Fernandez two minutes into stoppage time.
Also, 10-man Valencia salvaged a 1-1 draw at Sevilla, while Granada came from behind to beat visiting Deportivo La Coruna 2-1.
Karim Bellarabi scored the quickest goal in the 52-year history of the Bundesliga to help Bayer Leverkusen beat Borussia Dortmund 2-0 in the opening round on Saturday.
Bellarabi scored nine seconds after kickoff, beating the previous record of 11 seconds set by Giovane Elber for Bayern Munich in January 1998, Ulf Kirsten for Leverkusen in March 2002 and Paul Freier for Bochum in May 2003.
Bellarabi took a pass from Sebastian Boenisch, eluded Dortmund defender Matthias Ginter and slotted inside the left post from 12 yards.
Schalke let a one-goal lead slip by conceding twice in three minutes to lose to Hannover 2-1. Haris Seferovic's 15th-minute goal on his Bundesliga debut was enough for Eintracht Frankfurt to beat Freiburg 1-0 and Werder Bremen came from two goals down to draw 2-2 at Hertha Berlin. Hoffenheim defeated Augsburg 2-0 at home.
Bordeaux extended its perfect start to the season by rallying past Nice 3-1 on Saturday for a third straight victory in the French league.
Marseille beat Guingamp 1-0 to earn its first win of the season under Argentine coach Marcelo Bielsa, Lille kept a third straight clean sheet by defeating Lorient 2-0 and Bastia edged Toulouse 1-0 with a penalty from Ryad Boudebouz.
Promoted Caen stunned Reims 2-0 with late goals from N'Golo Kante and Herve Bazile, and Montpellier needed a free kick from Siaka Tiene and a header from Souleymane Camara to down promoted Metz 2-0.