Cristiano Ronaldo broke the deadlock in the 21st minute, latching onto James Rodriguez’s scooped ball through and firing a superb half-volley past Simon Mignolet for his 70th Champions League goal.
Ronaldo’s strike edged him within one of club icon Raul’s all-time Champions League goalscoring record.
It was one-way traffic after that as Karim Benzema headed Tony Kroos’ cross into the far corner before the French striker poked in a third after Liverpool failed to clear a corner.
Basel’s Serey Die was sent off in the 18th minute but the game looked to be heading for a goalless draw until defender Yordan Minev scored the decisive goal, meaning Ludogorets, Liverpool and Basel have three points each.
Karim Benzema scored twice after Cristiano Ronaldo broke his six-match goal duck at the ground with a superb opener to
Madrid’s first win – in fact first goals – in four meetings against the Reds came all too easily as they highlighted the gulf in class.
Olympiakos topped Group A after former Fulham midfielder Pajtim Kasami grabbed the winner in a 1-0 victory over Juventus.
The Greek champions are level on points with Atletico Madrid, who sit second after hammering Malmo 5-0 at the Vicente Calderon.
All the goals came in the second half as Koke, Mario Mandzukic, Antoine Griezmann, Diego Godin and Alessio Cerci secured a valuable three points for the Spanish champions.
Giulio Donati and Kyriakos Papadopoulos both scored in the second half as Bayer Leverkusen beat Zenit St Petersburg 2-0 to take charge of Group C.
Monaco climbed above Andre Villas-Boas’ side into second place as they drew 0-0 withBenfica, who earned their first point of the campaign.
Borussia Dortmund hammered Galatasaray 4-0 away from home to make it three wins out of three in Group D.
Pierre-Emerick Aubameyang scored twice in 18 minutes for the visitors, first tapping home Marco Reus’ pin-point pass before adding another from close range.
Reus put Dortmund out of sight before half-time with a stunning, curling shot before substitute Adrian Ramos added a fourth late on.
Arsenal look to be joining Dortmund in the knock-out phase after two late goals secured a remarkable 2-1 win at Anderlecht.
The hosts were on course for a shock victory when Andy Najar found the net with a brilliant header in the second half but there was late drama as Kieran Gibbs side-footed home an equaliser in the 89th minute before Lukas Podolski completed the turn-around with an emphatic finish in injury-time.
The win puts leaves Arsenal second, five points ahead of their opponents and three behind Dortmund.