Spain's Barcelona and Atletico Madrid stumbled and dropped their first points of the season, missing the chance to equal the record of the best La Liga start.
Bayer Leverkusen earned a controversial win at Hoffenheim courtesy of a 'phantom goal' by Stefan Kiessling and fellow German Mesut Ozil found the net in more conventional fashion as Arsenal took a two-point lead in the Premier League.
Champions Barcelona failed to score in a domestic league game for the first time in 65 matches when they were held to a 0-0 draw at Osasuna.
Atletico Madrid lost 1-0 at Espanyol as Real Madrid's record nine successive wins to kick off the 1968-69 campaign remained in tact.
Third-placed Real won 2-0 at home to Malaga to close to within three points of leaders Barca ahead of next week's 'Clasico' at the Nou Camp. Barcelona have 25 points from nine games, with Atletico on 24.
Real's victory came thanks to a goal from Angel Di Maria and a stoppage-time Cristiano Ronaldo penalty, won by world record signing Gareth Bale who was a late substitute.
Inter had goalkeeper Samir Handanovic sent off in the fifth minute for bringing down Alessio Cerci but his replacement Juan Pablo Carrizo saved the penalty.
They twice fell behind, hit back to lead 3-2 only to be denied a win by last-minute free kick from Nicola Bellomo at Torino.
Roma lead with 24 points, followed by Napoli and Juventus on 19 each.
Arsenal added more weight to their title credentials with a stylish 4-1 victory over Norwich City that included two goals from their record signing Mesut Ozil as they went two points clear at the top of the table.
Manchester City and Tottenham Hotspur are a further point behind after Sergio Aguero scored twice in a 3-1 win for Manuel Pellegrini's side at West Ham United and Spurs man-of-the-moment Andros Townsend netted in a 2-0 victory over Aston Villa.
Bayern Munich scored four second-half goals as they came from behind to beat Mainz 05 4-1 at stay top.
Shawn Parker gave the visitors a shock lead but last season's treble winners replied with two goals from Thomas Mueller and one each from Arjen Robben and Mario Mandzukic.
Bayern have 23 points from nine games, one ahead of Borussia Dortmund, who beat Hanover 96, and Bayer Leverkusen, who won 2-1 at Hoffenheim with a "phantom goal" by Stefan Kiessling.
The goal was awarded even though replays showed that Kiessling's header entered the net through a hole in the side. Hoffenheim have lodged an official protest.
Two goals each from Zlatan Ibrahimovic and Edinson Cavani helped Paris St Germain open up a two-point lead at top of the Ligue 1 standings thanks to a 4-0 hammering of Bastia at home.
Monaco squandered a two-goal lead at lowly Sochaux and slipped to second on 22 points following their 2-2 draw as new coach Herve Renard got off to an encouraging start with the struggling Easterners.
Lille are third on 20 points after Pape Souare's early goal gave them a 1-0 win at Montpellier.
FC Salzburg set a record for the longest unbeaten run in the Austrian Bundesliga on Saturday when they thrashed Wacker Innsbruck 6-0 to complete their 31st league match without defeat. (Compiled by Alison Wildey, editing by Ed Osmond)