German giants Bayern Munich are in second position, with 768 goals while Real’s rivals Barcelona is in third position with 655 goals.
The club has had some prolific goal scorers over the years, none more so than Cristiano Ronaldo who, during his nine seasons in Madrid, became the leading scorer in the tournament’s history, including the 105 goals he scored for Real Madrid.
Benzema’s two goals on Wednesday were his 74th and 75th Champions League goals, while club legend Raul has 66.
The European Cup was introduced in 1955, before it was rebranded to the Champions League in 1992.
Real Madrid has won the competition a record 13 times, including three times in a row between 2015 and 2018.
The club won the inaugural edition of the European Cup in 1955-56, as well as the following four editions before being knocked out by Barcelona in the first round in 1960.
Benzema’s goals proved decisive on Wednesday as Real beat Shakhtar 2-1 to maintain its push to qualify for the next round of the Champions League.