Real Madrid took a commanding lead in the first leg of the quarter-final after Benzema scored a hat-trick.
Carlo Ancelotti returned to the club where he won the FA Cup and the Premier League, after veteran France forward Benzema delivered his latest masterpiece.
Benzema, fresh from the hat- trick that sunk Paris St-Germain in the last 16, scored twice in the space of three minutes to give Real Madrid a 2-0 lead.
After a goal by Kai Havertz gave the Blues hope before the break, a poor clearance by Mendy gifted Benzema his third goal of the game to put Real in control of the tie before the second leg.
After they were hit by Benzema's brilliant one-two and then saw their hopes of mounting a comeback wrecked by a self-inflicted wound, they were always fighting an uphill task.
When Vinicius Junior hit the bar, Real warned about the danger they posed, but he provided the cross for Benzema to open the scoring.
When Benzema confirmed his aerial threat with a second, they were always vulnerable against a side who are masters of these situations.
The entire destiny of the tie may have changed in the opening 40 seconds of the second half, when Havertz gave a subdued Stamford Bridge some hope.
Mendy made an expensive mistake when he raced from goal to send a weak pass to Antonio Rudiger.
The defender was unable to control the ball and Benzema was able to roll the ball into the unguarded net with Mendy looking on.
The changes were undermined before they had a chance to take effect.
Romelu Lukaku was brought on in a desperate attempt to get the situation back but his struggles were summed up when he sent a weak head wide with one of the best chances of the night.
With Real holding a two-goal advantage going into the second leg at the Bernabeu, it would rank as one of their finest achievements if they were to reach the last four from this position.
Real Madrid may be the runaway leaders in La Liga, but they are considered to be rank outsiders as they chase a 14th triumph in the European Cup.
They demonstrated once again that their credentials are dismissed at their peril after the dramatic comeback against the odds to knock out Paris St-Germain in the last 16.
They have a leader who has demonstrated his expertise by winning this trophy three times with AC Milan and Real Madrid, and that leader is Carlo Ancelotti.
The coach and Real's players showed they are old hands at this and how they punished Chelsea, with Benzema and the 36-year-old Croatia maestro Luka Modric at their heart, to take a giant stride towards the semi-final.
Benzema gets better with age, scoring two goals of the highest class before scoring a third goal, while Modric retains that priceless ability to control the pace of games, retain possession and always make the right choice from the options available.
The veteran Italian, who flew into London on the day of the game after recovering from Covid-19, cut a very satisfied figure at the final whistle.
Formation 3-4-2.
4Christensen6Thiago Silva2Rüdiger24James7Kanté5Jorginho28AzpilicuetaFormation 4-3-3.
2Carvajal3Militão4Alaba23Mendy15Valverde9Benzema20Vinícius JúniorThe match ended with Real Madrid 3.
The second half ended with Real Madrid winning.
Foul by Kai Havertz.
The defensive half is where the free kick was won.
The person has a foul by the other person.
Vincius Júnior won a free kick in the attacking half.
An attempt was missed. The shot from the centre of the box is too high for Hakim. Romelu Lukaku assisted.
Foul by Antonio Rüdiger.
The defensive half is where the free kick was won.
The left wing is where Mason Mount won the free kick.
Daniel Carvajal is from Real Madrid.
There is a substitution for Real Madrid. There is an injury that has led to the substitution of Dani Ceballos.
There is a substitution for Real Madrid. Bale replaces Benzema.
Azpilicueta won the free kick in the defensive half.
The Real Madrid player had a foul.
The attempt was saved. The shot from outside the box was saved in the bottom left corner. It was assisted by Ruben Loftus-Cheek.
The attempt was blocked. The shot from the left side of the box by Mason Mount was blocked. Kai Havertz assisted.
The attempt was saved. Kai Havertz' shot from outside the box was saved in the top centre of the goal. The assistance was given by Mateo Kovacic.
César Azpilicueta was called for a foul.
The defensive half is where Daniel Carvajal won the free kick.