Luis Suarez helped Barcelona open its Spanish title defense with a 1-0 win over Athletic Bilbao on Sunday, while former Barca forward Pedro Rodriguez made a great start with Chelsea by scoring one goal and setting up another in a 3-2 win against West Bromwich Albion.
Real Madrid was held to a scoreless draw at recently promoted Sporting Gijon, while Manchester City beat Everton 2-0 to earn its third-straight win and retain its league lead in England.
Udinese stunned Italian champion Juventus 1-0 in Turin, and Borussia Dortmund defeated Ingolstadt with its second consecutive 4-0 win in the Bundesliga.
Here is a look at Europe's major leagues on Sunday:
Lionel Messi missed a penalty but Luis Suarez scored in the second half to give Barcelona a 1-0 victory over Athletic Bilbao in its Spanish league opener.
That gave the defending champion a small gap on archrival Real Madrid, as Rafa Benitez started his stint in charge with a 0-0 draw at promoted side Sporting Gijon.
Suarez netted the winner from close range after a long cross by Jordi Alba in the 54th minute at Bilbao's San Mames Stadium. Messi had a chance to open the scoring in the first half after a disputed foul on Suarez inside the area, but the Argentine playmaker had his low shot from the spot saved by goalkeeper Gorka Iraizoz.
A disappointing result in the opener would have raised more questions about Barcelona after an unusually difficult start to the season. The club was stunned by Bilbao last week in the Spanish Super Cup final, losing the title 5-1 on aggregate.
Pedro Rodriguez scored one goal and set up another in his first half-hour of Premier League football, setting Chelsea on its way to a 3-2 win over West Bromwich Albion and the first victory of its title defense.
League-leading Manchester City, meanwhile, earned its third straight win of the season - and a club record-equaling ninth victory in a row - by beating Everton 2-0 thanks to second-half goals by Aleksandar Kolarov and Samir Nasri. With eight goals scored and none conceded, it is an ominous start by a team looking for a third title in five seasons.
Liverpool is the only other team with a 100 percent start, ahead of its match at Arsenal on Monday that wraps up the third round.
Udinese stunned Juventus by winning 1-0 in Turin as the Italian champions' bid for a record-equaling fifth successive league title started with its first loss in 48 Serie A home matches.
Juventus dominated but was unable to finish any of its many chances and Udinese made the hosts pay when Cyril Thereau scored 12 minutes from time with one of his side's few opportunities.
Fiorentina eased past 10-man AC Milan 2-0, while Sassuolo beat Napoli for the first time in Serie A, coming from behind to win 2-1.
Inter Milan snatched a 1-0 win over 10-man Atalanta when on-loan Manchester City striker Stevan Jovetic curled a stunning strike into the top right corner in the third minute of stoppage time.
Japan midfielder Shinji Kagawa scored as Borussia Dortmund defeated Ingolstadt and claimed its second successive 4-0 win in the Bundesliga, while Borussia Moenchengladbach slumped to its second loss.
After dominating the first half and squandering several chances, Dortmund finally made the breakthrough through Matthias Ginter in the 55th minute. The defender took Henrikh Mkhitaryan's cross and left a defender sprawling with his first touch before scoring inside the far post with his next.
Marco Reus made it 2-0 with a penalty five minutes later after Moritz Hartmann fouled Marcel Schmelzer.
Kagawa scored in the 84th after fine work from Pierre-Emerick Aubameyang on the right.
Later Sunday, Mainz won 2-1 at Moenchengladbach, which was bottom of the table after two rounds.
Marseille stormed to its first points of the season as it thrashed newly-promoted Troyes 6-0 in its first match under new coach Michel.
Michel was only appointed on Wednesday to replace Marcelo Bielsa, who resigned over a contract dispute after the first match of the season.
Marseille had yet to score a goal this season going into the match, following two 1-0 defeats.
Lille and Bordeaux are still in search of their first win of the season after an entertaining 0-0 draw, which saw the woodwork hit four times.
Saint-Etienne moved to four points after snatching a 1-0 win at Lorient, which played almost the entire match with 10 men.
Lorient goalkeeper Benjamin Lecomte was sent off after just 42 seconds for bringing down Nolan Roux just outside the area, when the Saint-Etienne striker was clean through on goal.