Early goals from Saul and Antoine Griezmann gave Diego Simeone’s men realistic hope of hauling back a 3-0 first-leg deficit before a goal from Isco late in the first half effectively ended the contest.
And it was Frenchman Benzema who shone brightest as Real ultimately cruised to a 4-2 aggregate win, setting up Isco’s effort and having a major impact on a much more consistent second-half showing from his side.
The hosts had been indebted to goalkeeper Jan Oblak for keeping their slim hopes alive in the early stages when the Czech made a brilliant one-handed save to deny Casemiro.
But Simeone’s men would capitalise on their lucky escape and pulled their first goal back after 12 minutes when Saul rose highest in the box to power home from a Koke corner.
The goal raised hopes of a sensational comeback and they were further realised four minutes later when Atletico reduced their aggregate deficit to a single goal.
Sweeping irresistibly forward, Fernando Torres was fouled by Raphael Varane in the box and Griezmann calmly slotted the resulting penalty past Real goalkeeper Keylor Navas.
Simeone’s intentions were clear on the sidelines as he urged his team and supporters on, but Real drew on all of their Champions League experience to weather the storm and limit the damage from the early spell of pressure.
And the visitors grabbed what would prove to be a crucial goal three minutes before the break when Isco fired home after a moment of magic from Benzema tight on the left flank.
Benzema wriggled out of a seemingly impossible situation surrounded by three Atletico defenders and crossed for Toni Kroos, whose initial effort was blocked by Oblak before Isco shot home the rebound. The goal took the sting out of Atletico who, from the cusp of an improbable leveller, suddenly found themselves needing to score five times on the night to give themselves a chance to advance.
Real started the second period on top, with Ronaldo’s free-kick from a tight angle well saved by Oblak, but Atletico were in no mood to give up as Griezmann looped a free-kick just over the crossbar.
Kevin Gameiro also should have done better on the end of a swift Atletico counter-attack but Cristiano Ronaldo, in particular, was growing in prominence and was unlucky to have a 69th-minute effort incorrectly ruled out for offside.
Griezmann forced a fine save out of Navas while the brilliant Benzema saw a diving header flash inches wide as the rain poured down and Real played out the final quarter of an hour to ease into a final place.
Oblak, Gimenez (Thomas 57), Savic, Godin, Filipe Luis, Koke (Correa 76), Gabi, Saul, Carrasco, Torres (Gameiro 56), Griezmann.
Miguel Moya, Tiago, Lucas, Gaitan.
Navas, Danilo, Sergio Ramos, Varane, Marcelo, Kroos, Casemiro (Lucas 76), Modric, Isco (Morata 87), Benzema (Marco 77), Ronaldo.
Casilla, Nacho, Rodriguez, Kovacic.
Cuneyt Cakir (Turkey).