Cristiano Ronaldo scored twice to lead Real Madrid 3-0 over APOEL here in the inaugural 2017-2018 Champions League football match for both clubs, while Manchester City got their campaign off to a great start with a 4-0 drubbing of Feyenoord.
After two successive draws in La Liga, the Blancos were in need of a win on Wednesday, reports Efe news agency.
With Karim Benzema hurt and Gareth Bale unsteady, the fans at the Santiago Bernabeu were also anxious for the return of Ronaldo, sidelined from La Liga play by a suspension.
The Portuguese international did not disappoint, scoring in open play and from the spot to keep pace with Barcelona's Lionel Messi in the contest for the Champions League goals crown.
Sergio Ramos scored the third goal as Real Madrid dispatched a clearly weaker APOEL side.
The outcome leaves the Blancos in first place in Group H - this year's "Group of Death" - by virtue of a better goal difference than Tottenham Hotspur, who beat Borussia Dortmund 3-1 at London's Wembley Stadium.
The hosts took the lead on a goal by Heung-Min Son, but Dortmund pulled level with Andriy Yarmolenko's strike from distance before hometown hero Harry Kane scored a pair to give Spurs the victory.
Man City claimed first place in Group F after clobbering Feyenoord 4-0 in Rotterdam. The Citizens led 3-0 before the half-hour mark, thanks to goals from John Stones, Sergio Agero and Gabriel Jesus.
Stones later added a second goal.
Napoli, who were expected to be City's main rival in the group, lost 2-1 away to Shakhtar Donetsk.
Sevilla began the day having never won a European match on English soil and ended it in the same condition.
The Spanish side struck first against Liverpool at Anfield, as Wissam Ben Yedder scored in the 5th minute. Roberto Firmino answered for the Reds in the 21st minute and Mohamed Salah put the hosts up 2-1.
Firmino hit the post from the spot when he had a chance for the 3-1 just before half-time and Joaquin Correa got the late equalizer for Sevilla to make the final score 2-2.
Wednesday's other Group E match also ended in a draw, as Maribor and Spartak Moscow deadlocked 1-1.
The surprise of the day came courtesy Besiktas, who stunned hosts Porto 3-1 on goals by Anderson Talisca, Cenk Tosun and Ryan Babel to take the lead in Group G, where Monaco and RB Leipzig drew 1-1.
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