Eden Hazard ended Real Madrid's drought in a match that coach Zinedine Zidane missed after he contracted the coronavirus.
Meanwhile, Lionel Messi and Antoine Griezmann each scored twice as Barcelona thrashed Granada 4-0 away to win a third consecutive La Liga game for the first time this season.
Real Madrid's second consecutive defeat comes ahead of Saturday's Clasico and at the hands of Ukrainian champions Shakhtar, who were without 10 first-team players and nine members of staff due to coronavirus infections.
Real Madrid have been crowned La Liga champions for the 34th time after Karim Benzema scored twice in a 2-1 victory over Villarreal which clinched the title with one game to spare.
Substitute Ivan Rakitic scores in the 71st minute to help Barcelona win 1-0 against Athletic Bilbao bringing the Catalans back to the top of the La Liga. Second placed Real Madrid face Real Mallorca on Wednesday.
Real's victory means they lead the standings on 56 points after 26 games, with Barca slipping to second spot on 55.
Gabriel Jesus scored an equaliser in the 78th minute and Kevin De Bruyne netter an 83rd-minute winner from the penalty spot as Man City came from behind for a 2-1 win over Madrid in the first leg of the last 16 at the Bernabeu Stadium on Wednesday.
The visitors scored a goal in the 18th minute and despite not having a dominating presence, managed to take home 3 points. The win places Real Madrid second in group A, while the home team ends up with the group's bottom spot.
Unbeaten Real are a point ahead of promoted Granada and Atletico Madrid after Diego Simeone's side failed to break down their well-drilled local rivals.
Real Madrid climbed to the top of the standings with 14 points from six games, one point and one place ahead of Atletico Madrid, whom they face on Saturday in the derby at the Wanda Metropolitano.
Veteran Croatian playmaker Luka Modric heroically helped drag his country to the World Cup final in Moscow and battled hard to lead his club Real Madrid to their second consecutive Champions League crown.
The French team of 2018 is truly multicultural and should be celebrated across France. A number of African countries can also take pride in the victory.
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