Bayern Munich went top of the Bundesliga and Andrea Pirlo was in sparkling form as Juventus beat AC Milan, but the true stars were Barca and Atletico in Spain and Roma in Italy, who have now won eight, eight and seven consecutive league matches since the start of the season.
Arsenal's win streak in England came to an end as they dropped points for the first time since the opening day of the season, while in France Paris St Germain got the better of bitter rivals Olympique Marseille in Ligue 1 and keep pace with Monaco at the top.
Alexis Sanchez struck twice and created a goal for Neymar as Barcelona recovered from conceding early to maintain their perfect La Liga start with a 4-1 win at home to Real Valladolid on Saturday.
An eighth victory in eight games for the champions restored their five-point advantage over arch-rivals Real Madrid who needed a Cristiano Ronaldo goal in the fourth minute of stoppage time to secure a 3-2 triumph at Levante earlier.
Atletico Madrid kept pace with Barcelona with Diego Costa scoring both goals in a workmanlike 2-1 victory over Celta Vigo on Sunday.
A breakaway goal from Alessandro Florenzi completed the rout to leave Roma on 21 points from seven games and making them early title favourites.
Napoli demolished promoted Livorno 4-0 while goals from Andrea Pirlo, Sebastian Giovinco and Giorgio Chiellini gave Juve a 3-2 win over Milan, who had taken the lead through Sulley Muntari after 20 seconds. Muntari also scored Milan's consolation.
Treble winners Bayern Munich reclaimed top spot in the Bundesliga despite a 1-1 draw at Bayer Leverkusen.
Franck Ribery beautifully set up Toni Kroos for Bayern's 30th-minute lead but Leverkusen, a point behind on 19 in third place, struck straight back through Sidney Sam.
Bayern, who were the better team throughout and missed half a dozen clear scoring chances, have 20 points from eight matches, one ahead of Dortmund and third-placed Leverkusen.
The Bavarians, who were last beaten in the league by Leverkusen last year, have now gone 33 league games without defeat - three shy of the record.
Dortmund slipped down to second after missing a bagful of chances themselves and conceding two late goals to slump to a 2-0 defeat at Borussia Moenchengladbach for their first loss of the campaign.
Monaco retained their Ligue 1 lead as James Rodriguez set up both goals in a 2-1 home win against St Etienne on Saturday.
Rodriguez fed Yannick Ferreira Carrasco and Lucas Ocampos to put the principality's side on 21 points from nine matches.
They lead Paris St Germain on goal difference as the French champions snatched a 2-1 comeback win at Olympique Marseille despite playing with 10 men for an hour.
Zlatan Ibrahimovic scored the winner from the penalty spot.
Marseille are now fourth on 17 points.
Arsenal returned to the top of the Premier League on Sunday after Jack Wilshere rescued a point for them in a 1-1 draw at West Bromwich Albion, but rivals Liverpool, Chelsea and both Manchester clubs all made up ground with wins.
Liverpool are level on points with Arsenal after strikers Luis Suarezand Daniel Sturridgeboth scored for the second week running on Saturday in a 3-1 win at home to Crystal Palace, while Chelsea won at Norwich by the same scoreline to go third.
Jose Mourinho's team were 1-1 until the dying stages of Sunday's match but a raft of attacking substitutions and late goals from Eden Hazard and Willian helped give them a comfortable victory.
Manchester United's conveyor belt of exciting young players seems still to be in working order after 18-year-old Adnan Januzaj struck twice as they came from behind to beatSunderland 2-1, avoiding a third straight league defeat.
FC Salzburg equalled Rapid Vienna's 26-year-old Austrian Bundesliga record of 30 matches unbeaten when they won 2-1 at champions Austria Vienna.
Salzburg have not lost a league game since their defeat against SV Ried in November last year.
Brazilian Alan scored the second-half winner for Salzburg with his eighth goal of the season to take them on to 25 points from 11 games, six clear of second-placed Ried.
Leaders Basel went three points clear of Grasshoppers at the top of the Swiss Super League when they came from behind to win 2-1 at Lausanne Sport despite playing most of the second half with 10 men.
Salim Khelifi gave the hosts a 14th minute lead and Basel pulled level with an own goal by Kevin Fickentscher six minutes before the break.
Basel's Ivorian forward Giovanni Sio was sent off after clashing with Lausanne captain Guillaume Katz in the 50th minute, but Arlend Ajeti grabbed a winner on the hour. Grasshoppers drew 1-1 at FC Thun.