Barcelona and Real are among four teams with a perfect record in Spain while it is even more tight in Serie A, with five clubs sharing top honours, including champions Juventus.
Daniel Sturridge scored after four minutes at Anfield on the day the club celebrated the 100th birthday of renowned former manager Bill Shankly, a result that sent them to the top of the table with three wins from three matches.
Arsenal prevailed over big-spending north London rivals Spurs shortly before Bale's move to Real Madrid for 100 million euros ($131.86 million) was confirmed.
Olivier Giroud netted for the Gunners, and like Sturridge has scored three goals in three appearances this season.
Chelsea, who lost the Super Cup to Bayern Munich on Friday, lie second, two points behind Liverpool, while Manchester City, 2-0 winners over Hull City on Saturday, Arsenal, Stoke and Spurs lie on six points. Champions United have four.
Lionel Messi struck the third first-half hat-trick of his career as Barcelona extended their winning start to their title defence with an entertaining 3-2 win at Valencia.
Hours before sealing the transfer of Bale from Tottenham Hotspur, Real Madrid made it three wins from three by beating Athletic Bilbao 3-1 at the Bernabeu and Atletico Madrid joined the two giants on nine points with a 2-1 success at Real Sociedad.
Promoted Villarreal's impressive 3-0 victory at Osasuna means they also have a perfect record and suggested the team known as "yellow submarine" are unlikely to surrender their top flight status again this term.
At the age of only 26, World Player of the Year Messi is now the sixth highest scorer in La Liga history with 220 goals, surpassing Quini's 219 and closing in on the record of 251 held by Telmo Zarra.
Arturo Vidal scored twice and Carlos Tevez added another goal as Juventus completed an impressive 4-1 win over 10-man Lazio.
Napoli also made it two victories from two games, overcoming Chievo 4-2 in Verona with two goals from in-form Slovakian Marek Hamsik and Gonzalo Higuain's first Serie A strike.
Henrikh Mkhitaryan scored his first two goals for Borussia Dortmund since his 27.5 million euro move to give them a 2-1 win at Eintracht Frankfurt which maintained their 100 percent Bundesliga record.
The Armenian's goals were both excellently taken as he side-footed the first past Kevin Trapp and then rifled in a 25-metre effort from the edge of the penalty area early in the second half.
VfB Stuttgart, beaten in their first three Bundesliga outings, burst into life with a 6-2 win over Hoffenhaim in the other game, inspired by a hat-trick from striker Vedad Ibisevic.
Dortmund's win left them top of the Bundesliga as the only team with 12 points from their first four games. Defending champions Bayern Munich, who drew with Freiburg on Tuesday, are two points behind in second with Hanover, Bayer Leverkusen and Mainz 05 on nine each.
Emmanuel Riviere came off the bench to score his fifth goal in four games as big-spending Monaco underlined their title ambitions by climbing to the top of Ligue 1 with a 2-1 victory at Olympique Marseille.
Riviere secured the win in the 79th minute as unbeaten Monaco, who have splashed out around 170 million euros to build a star-studded squad, leapfrogged Marseille to the top of the standings with 10 points from four games.
Marseille are second with nine points, ahead of St Etienne on goal difference. St Etienne defeated Girondins Bordeaux 2-1 at home.
Champions Paris St Germain are fourth, one point behind, after beating promoted-side Guingamp thanks to two injury-time goals by Adrien Rabiot and Zlatan Ibrahimovic.
Striker Stef Nijland struck the equaliser as PEC Zwolle came from a goal down to draw 1-1 with FC Utrecht and stay top of the Dutch league with 13 points after five games.
PEC lead the table by two points from PSV Eindhoven, who were also held to a home draw during celebrations for their 100th birthday.
Zulte Waregem scored an injury time winner to edge Anderlecht in a see-saw game which produced seven goals and three red cards.
Sacha Kljestan struck first for Anderlecht and Thorgan Hazard replied for Zulte as the first half ended 1-1.
Hazard had a penalty saved by Silvio Proto early in the second half after Anderlecht's Cheikhou Kouyate was controversially dismissed but Olafur Skulason put Zulte ahead seconds later, then Matias Suarez equalised, before Skulason was sent off for elbowing.
Zulte went 3-2 up with a Karel D'Haene header from Hazard's corner, Demy De Zeeuw made it 3-3 for Anderlecht, who then had Olivier Deshacht sent off for a second bookable offence and went home pointless after Franck Berrier headed the winner.
Zulte are second with 14 points from six games, four behind leaders Standard Liege who maintained their 100 percent record by beating Kortrijk 2-0.
FC Sion finally scored their first league goal of the season, 14 minutes into their seventh match, as they beat promoted Aarau 1-0.
Brazilian Leo Itaperuna ended their 553 minutes rate when he scored following a corner.
Young Boys Berne stayed top of the Swiss Super League despite losing 2-1 at champions FC Basel, who are three points behind them alongside Grasshoppers.
Rene Gartler scored a hat-trick as SV Ried won 4-1 at Admira Wacker to pull level with FC Salzburg at the top of the table.
Salzburg were held to a 1-1 draw at home by Rapid Vienna after Stefan Hierlaender gave the hosts the lead just before halftime and United States forward Terence Boyd levelled in the second half for the visitors.
Ried and Salzburg are both unbeaten after seven games and have 15 points apiece. Promoted Groedig lost 6-3 at home to Wiener Neustadt and champions Austria Vienna were held 1-1 at home by Wacker Innsbruck.
Greece striker Kostas Mitroglou scored a second-half hat-trick as champions Olympiakos Pireaus maintained their perfect start to the Super League with a 5-0 rout at Levadiakos.
The Piraeus club lead the table with nine points ahead of newly-promoted AEL Kalloni and PAOK Salonica, who both have six points.
($1 = 0.7584 euros) (Compiled by Pritha Sarkar; Editing by John Mehaffey)