Goals from Mason Mount, Antonio Rudiger and Timo Werner overturned Real Madrid’s 3-1 advantage from the first leg last week, but Rodrygo’s sublime volley forced the tie into extra time.

Benzema, who scored a hat-trick at Stamford Bridge, had the final say, though, thundering home a header six minutes into extra time to seal a 5-4 aggregate victory. 

Carlo Ancelotti's side will now face either Atletico Madrid or Manchester City, with Pep Guardiola’s side holding a 1-0 lead from the first leg.

Chelsea's strong start was rewarded in the 15th minute when Mount curled past Thibaut Courtois from just inside the penalty area after latching onto Werner's nudged ball forward.

Madrid struggled to break Chelsea's stubborn backline down in the first half, with Ancelotti's men going in at the break without a shot on target to their name. 

Chelsea levelled the tie on aggregate six minutes into the second half, Rudiger planting a powerful header past Courtois from Mount's cross. 

Alonso thought he had edged Chelsea in front 11 minutes later when he thumped into the top corner from eight yards, yet his effort was ruled out for handball following a VAR check. 

Benzema crashed a header against the crossbar soon after, before Werner put Chelsea ahead on aggregate in the 75th minute with a strike that proved too hot for Courtois to handle. 

Madrid clawed their way back into the tie with 10 minutes remaining, though, as Rodrygo, who had only been on the pitch for two minutes, steered a superb volley past Edouard Mendy from Luka Modric's breathtaking cross. 

That set the stage for Benzema's decisive goal in additional time, the France international heading past Mendy from 10 yards out following fine work down the left by Vinicius Junior.