Felix Nmecha scored twice and Fábio Silva grabbed another as Borussia Dortmund won 3-0 at home to promoted Paderborn to continue their perfect start in the Bundesliga. Dortmund’s win made it three from three in the league this campaign, their best start in 11 seasons, dating back to Thomas Tuchel’s time.

Starting up front alongside Serhou Guirassy for the first time this season, Silva converted a clever pass from the Guinean to give the hosts the lead after five minutes. Guirassy had two goals disallowed for offside in the first half but Dortmund were rarely troubled by the toothless visitors, who are yet to score since returning to the top flight.

Nmecha came off the bench to score twice, wrapping up victory for the hosts with a stunning late bicycle kick.

Dortmund captain Nico Schlotterbeck made his first appearance since picking up an ankle injury at the World Cup and told Sky Germany he kept his comeback under wraps. “We just hadn’t communicated that much yet because I didn’t want to,” Schlotterbeck said, adding “I missed it terribly. It was a serious injury but I’m glad to be back now.”

Freiburg thumped a poor Borussia Mönchengladbach 5-0 at home to climb to the top. Yannik Engelhardt and Igor Matanovic netted twice each and Maximilian Eggestein added a late fifth as the hosts sent Gladbach, who finished with 10 men, to the foot of the table.

A 2-2 home draw with Bayer Leverkusen ended Augsburg’s short stint as leaders. Augsburg were top after the last matchday for the first time in their history but were held by Leverkusen despite a double from Michael Gregoritsch.

Eintracht Frankfurt won their first match of the campaign with a 3-1 victory at neighbouring Mainz, with Can Uzun’s double either side of a Jonathan Burkardt goal. Frankfurt’s goalkeeper Noah Atubolu kept his remarkable penalty-saving record alive when he stopped a first-half effort from Nadiem Amiri. Atubolu’s save was his sixth in a row, extending his own Bundesliga record.

West Ham loanee Niclas Füllkrug kept his excellent run of form since returning to the Bundesliga going, scoring the equaliser for Werder Bremen in a 1-1 draw at Cologne. Thijs Dallinga missed a penalty after eight minutes but teammate Linton Maina put Cologne ahead moments later.

Füllkrug’s goal came in the 69th minute and is his third in four games since returning to Germany. He only found the net three times in 29 matches for West Ham and scored just once in 20 games on loan at Milan last season.

Elsewhere, Hoffenheim won 2-1 at home against Stuttgart thanks to a double from Adam Hlozek. On Sunday, Bayern Munich travel to promoted Elversberg – who have a 100% record – while RB Leipzig host Hamburg.

In Spain, Kylian Mbappé scored twice ⁠as Real Madrid enjoyed a 4-1 victory over Rayo Vallecano ⁠in La Liga ⁠at ​the Santiago Bernabéu. Goals from Álvaro Carreras and Jude ⁠Bellingham made the result comfortable for José Mourinho’s side.

A 14th-minute ⁠penalty from Mbappé was followed three minutes ​later by ‌a simple finish ‌from Carreras, with Mbappé turned provider ‌this time. A relaxed Real found little resistance from Rayo thereafter and, 11 minutes before half time, Vinícius Júnior raced down the left to set up ‌Bellingham for a neat finish into the corner.

Six minutes into the ​second half, Sergio Camello pulled a goal back for Rayo following sloppy Real Madrid play. Despite whistles from the ⁠home crowd, Real kept Rayo at ​bay, ​before closing out the ​game with a 90th-minute goal ​from ‌Mbappé.

The result ​moved ​Real on to 12 points, level with leaders Barcelona, who have a game in hand. Barça are at Levante on Sunday afternoon. Alavés missed the chance to go top overnight with a 2-1 defeat at Racing Santander.

In Italy, Diego Moreira scored twice as Milan came from two goals down to hold early season Serie A pacesetters Lazio 2-2 in Rome on Saturday. Moreira came off the bench at half-time and hauled Milan level after Matteo Cancellieri and Tijjani Noslin had given the hosts the lead at the interval.

Despite losing their 100% record having started the season with three wins, Gennaro Gattuso’s side move to the top of the table. Ruben Amorim’s Milan are fourth on eight points, after also drawing last weekend at Juventus.

Cancellieri opened his account for the campaign after 10 minutes when he connected with a Mattia Zaccagni cross. A dominant Lazio had good chances to pull further clear before Noslin doubled their lead after 39 minutes with a close-range finish.

Amorim attempted to stem the tide by making three substitutions at half-time, bringing on playmaker Christian Pulisic and Moreira. His changes bore fruit after 65 minutes as Moreira volleyed home to halve the deficit. Less than two minutes later, the former Strasbourg player equalised with a fierce strike from outside the box, but neither side could find a late winner.

Atalanta slumped to a 2-1 defeat at home to Cagliari, with Sead Kolasinac handling the ball in the box to concede a second-half penalty that gave the visitors the win. Cagliari took the lead in the 19th ⁠minute when 19-year-old forward Paul Mendy rattled in the opener off the underside of the crossbar, ​but Gianluca Scamacca levelled for the home side ​four minutes before the break.

Mendy had the ​ball in the net again early in the second half only for the goal to be ruled out ​for a narrow offside, but ‌they took the lead ​again after Kolasinac was penalised, ​Daniel Maldini firing home from the spot to secure the three points.

The result moved Cagliari up to fourth in the table with nine points from their four games, while Atalanta are in ninth spot on six points. Earlier, hosts Genoa, who have yet to win this season, were held 1-1 by newly promoted Frosinone, who have seven points.

Champions Inter host Udinese on Monday, with Roma heading to Torino and Como at home to Parma. Inter and Roma have both won each of their first three matches.