Rangers ended Old Firm rivals Celtic's Scottish Cup dominance and took a big stride towards completing the double with a 2-0 victory at Ibrox.
Steven Davis opened the scoring with an acrobatic strike and a first-half Jonjoe Kenny own goal put the Premiership champions well on course for the last eight.
There was no way back for the Hoops, who had lifted the trophy in the previous four seasons, and Allan McGregor saved Odsonne Edouard's penalty as they suffered a first defeat under caretaker boss John Kennedy.
Victory for Rangers ensured they have won three and drawn one of their four clashes against their fierce city rivals in what has been an outstanding season.
Davis gave Rangers the lead in style in the 10th minute, volleying in from close range when Joe Aribo's deflected shot looped up invitingly for the midfielder following a sharp turn and incisive run from Ryan Kent.
Edouard shot straight at Allan McGregor after creating space for himself in the Rangers penalty area, then Callum McGregor's drive deflected over the crossbar and Stephen Welsh somehow failed to finish as Celtic pressed for an equaliser.
Steven Gerrard's side doubled their lead 12 minutes before half-time, though, with Aribo conjuring up some trickery to beat Diego Laxalt before crossing from the right and Kenny turned into his own net attempting to prevent Kent from slotting home.
Celtic should have reduced the deficit when Mohamed Elyounoussi was superbly denied by Allan McGregor and Edouard volleyed wastefully over following up.
The Gers keeper did brilliantly to race off his line and thwart Elyounoussi soon after, the Celtic forward letting himself down with a poor first touch after Edouard set him up.
Allan McGregor then dived to his right to keep out Edouard's spot-kick 11 minutes from time after Aribo was adjudged to have fouled Leigh Griffiths, which summed up Celtic's afternoon.
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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