In the first 20 minutes, Liverpool rolled back the clocks to go 2-0 up with goals from Darwin Nunez and Mo Salah. They showed the real intensity that Klopp's team was known for but has been seriously lacking this season.
Yet last year's finalists were even at the break after Vinicius Junior's brilliant 21st-minute strike and a comical clearance from Alisson that gifted the Brazilian his second.
Eder Militao headed in Luka Modric's free-kick just two minutes after the break and Real never looked back from there with a Benzema double pressing home their vastly superior second half. This leaves Liverpool needing a miracle if they are to progress to the quarter-finals.
Elsewhere, RB Leipzig held Manchester City to a draw as City failed to make their first-half dominance count with Josko Gvardiol's 70th-minute header cancelling Riyad Mahrez's earlier finish.
Napoli continues to look impressive, easily dispatching Eintracht Frankfurt 2-0, striker Victor Osimhen once again proving why he is so in demand.
The big story in the Europa League was Manchester United's comeback at Old Trafford which dumped La Liga leaders Barcelona out of the competition. Second-half goals from Brazilian duo Fred and Antony saw the Red Devils edge the tie 2-1 on the night and 4-3 on aggregate, booking their place in the last-16.
The likes of Juventus and Sporting Lisbon also progressed along with Union Berlin who continued their remarkable form, knocking out Dutch Champions Ajax.