Leading 2-1 from the first leg, City extended their lead through Raheem Sterling’s goal from close-range after Raphael Varane’s mistake.
Benzema equalised on the night with a header but Manchester City Brazil forward Gabriel Jesus made it 4-2 on aggregate after another shocking error by Varane.
Manchester City will play Lyon or Juventus in a one-off quarter-final tie on 15 August.
It is the third straight season Pep side, who finished second in the Premier League table, have reached the last eight in Europe’s premier club knockout competition.
Manchester City, seeking to win the Champions League for the first time, have not pass the semi-finals since 2015-16.
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