Rodrygo's double helped Real Madrid strengthen their position at the top of the table in LaLiga as Athletic Bilbao were beaten 2-0 at the Bernabeu.
The hosts went ahead just eight minutes into the game through Rodrygo's excellent top corner finish and an energetic start to the second half saw Brahim Diaz go close twice either side of Inaki Williams' strike, but Jude Bellingham's neat pass set the Brazilian up for his second in the 73rd minute to seal the three points.
Real remain at the summit, eight points clear of second-placed Barcelona, while Athletic remain fourth.
Although Athletic started the brighter of the two teams, Real struck with their first attack of the game when Brahim broke forward and dispatched a fantastic cross-field ball into Rodrygo, who cut in from the left to curl the ball sweetly from the outside of the box into the top corner.
The hosts settled into the game after their early goal, with Brahim having plenty of involvement on the right flank, but Athletic were handed an early blow when Yeray Alvarez Lopez was taken off with injury in the 24th minute and Daniel Vivian came on to replace him.
Toni Kroos' deflected 34th minute strike was comfortably claimed by Julen Agirrezabala and moments later the German international's corner was cleared as far as Federico Valverde, who chipped the ball from long-distance towards the bottom left corner but Agirrezabala made a quick low save.
The hosts pushed for a second in the closing stages of the first half when Brahim pounced on a loose ball and his cross was poked just wide of goal by Vivian and Real threatened again from the resulting corner when Aurelien Tchouameni headed just wide.
Real were straight out of the blocks after the break and nearly doubled their lead following a mazy run from Rodrygo, who cut in from the left and played the ball through to Brahim on the right, but his low shot rattled off the far post.
Athletic had a brilliant chance seven minutes into the half when Berenguer's corner picked out an unmarked Williams at the far post, but Andriy Lunin palmed away before Brahim threatened again at the other end, firing over the crossbar.
Real extended their lead in the 73rd minute when a quick ball from Bellingham picked Rodrygo out in plenty of space on the left and the Brazilian cut into the centre to coolly slot home into bottom corner.
Athletic had two great chances when Iker Muniain's flicked effort was collected by Agirrezabala and after finding some space Williams dragged a shot wide.
Eder Militao made his first appearance in seven months since picking up a cruciate ligament injury after coming off the bench in stoppage-time as Real comfortably saw out the win.
Leipzig have 'everything you would want' – Celtic boss Rodgers
Celtic may be four points clear of RB Leipzig in the Champions League, but Brendan Rodgers is not underestimating the challenge that his side face on Tuesday.
The Hoops welcome Leipzig to Celtic Park on matchday four, for what will be the fifth meeting between the sides.
Leipzig have won three of the previous four encounters, with Celtic winning 2-1 in a Europa League match in November 2018.
While Leipzig, who are second in the Bundesliga, have lost all of their Champions League matches this term, Celtic bounced back from their heavy defeat to Borussia Dortmund by holding Atalanta to a 0-0 draw in their last European outing.
Rodgers' team come into Tuesday's clash on the back of a resounding 6-0 defeat of Aberdeen in the Scottish Premiership, but Rodgers knows his side are in for a stern test.
"Leipzig are no different to Borussia Dortmund and Atalanta," said Rodgers. "A top team. They have everything you would want - speed, power, technique.
"It's a brilliant challenge for us."
After conceding seven goals against Dortmund on MD2, Rodgers explained Celtic knew they had to step up.
"You always have to learn and be better and we were against Atalanta, a really outstanding team," said Rodgers, who were perhaps fortunate not to concede against the Serie A side, given they conceded 2.4 expected goals (xG).
"We'll look to bring our energy to the game but we also know we'll have to defend for good periods of the game, play with concentration and commitment like we did against Atalanta," he said.
"There will be moments when we press with aggression and moments where we have to be controlled. Top teams will push you back and you have to have resilience."
After a run of 12 home games without a win at Celtic Park in the Champions League between 2013 and 2023 (D3 L9), Celtic have won their last two home games. They last had three wins in a row back in November 2007 under manager Gordon Strachan.
"Home games are very important at this level and when you want the result the supporters can bring you closer to that," said Rodgers.
"What the noise generates here is absolutely incredible.
"We will also need that bit of patience as well because we have to be educated in our pressure.
"We've got ourselves into a really good position after three games and now we have another opportunity to show we can pick up a result against a top team."
Neymar does not believe latest injury is serious
Neymar does not feel his latest injury is anything to be overly worried about.
The Brazilian star had to be substituted off late on in Al-Hilal's 3-0 win over Esteghlal in the AFC Champions League Elite on Monday.
Aleksandar Mitrovic's hat-trick propelled Saudi Pro League giants Al-Hilal to a comfortable win, though it was soured when Neymar clutched his right thigh and left the field just 29 minutes after coming on as a second-half substitute.
It was only the 32-year-old's second appearance since he returned from a year-long lay-off due to a serious knee injury.
However, the former Paris Saint-Germain and Barcelona attacker allayed fears over a serious injury.
"It felt like a cramp, only very strong!" Neymar posted on Instagram. "I'm going to have some tests and I hope it's nothing too serious.
"It's normal for this to happen after a year, the doctors had already warned me, so I have to be careful and play more minutes."
Neymar has played only seven games for Saudi Arabia's Al-Hilal since joining from PSG in a blockbuster transfer last year.
Fonseca targets statement Milan win over Real Madrid
Milan have no need to fear Real Madrid and their coach Paulo Fonseca is targeting a statement win in the Champions League.
Despite having won more Champions League/European Cup titles (seven) than any other club apart from Madrid (15), it has been 17 years since Milan last lifted the trophy in 2007.
On the other hand, holders Madrid have won the Champions League six times since 2013-14.
But Fonseca sees no reason to fear Los Blancos at the Santiago Bernabeu, where Carlo Ancelotti's side were recently hammered 4-0 by Barcelona.
"We're playing against a team that aspires to win the Champions League every year and for us it's a great opportunity to grow," Fonseca said.
"We'll play without fear of anything, with courage, because we believe we can play a great game and do great things.
"I always transmit to my team the desire to win and tomorrow will be no different. Real Madrid are a great team, but we will go out there thinking about winning. After that, anything can happen, but that's the mentality.
"To win a match like this, we have to defend well, have possession of the ball and create dangerous situations. A match against Real Madrid is a chance to show the world our quality and the way we are growing."
Madrid are 12th in the 36-team Champions League table with six points, while Milan are languishing in 25th spot – just outside the play-off places – with three points after three games.
Fonseca explained Milan had carefully studied Barcelona's 4-0 win over Madrid in last month's Clasico.
"I saw the derby, it's impossible not to watch it. They are teams I like to watch and I paid close attention to the game," Fonseca said.
"We are different from Barcelona but it was important to see Real Madrid's intentions against them because Barca have a similar way of defending with us. We made the whole team watch the game.
"It is the match between the two clubs that have won the Champions League the most. There are many games in the continent that are big, but this one is obviously something special, a match between two clubs that are attractive.
"We hope to put on a good show for people who enjoy good football."
Milan are winless in their last three Champions League games against Madrid (D2 L1) since they won 3-2 in October 2009 with goals from Andrea Pirlo and Alexandre Pato.
Madrid have won five of their seven home matches against Milan in the competition (D1 L1), beating them 2-0 in the most recent such match in October 2010.
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