The visitors only needed one more goal to progress to the final via aggregate, however they could not find the decisive score even with the benefit of five minutes of added time.
Real Madrid are the defending champions and are the favourites for many to reach yet another grand final.
But Benzema's double in between, the first a header, the second a simple finish following a awful error from Bayern goalkeeper Sven Ulreich, proved enough as Real hung on for a 2-2 draw, and a 4-3 win on aggregate.
For a second consecutive year, Bayern left the Bernabeu - and the competition - cursing their luck and refereeing decisions.
Real Madrid manager Zinedine Zidane (top R) looks on during the team's practice session at the Valdebebas training ground on Monday. But they shot themselves in the foot at the start of the second half, when Sven Ulreich, deputising for Manuel Neuer, could not get rid of a loose pass from Corentin Tolisso.
Both teams had chances go begging after that. Keylor Navas made a spectacular save on David Alaba from a tight angle just moments after Madrid's goal.
At the other end, Ronaldo had two close-range chances inside 30 seconds but could take neither.
The Argentine added: "Real Madrid is a club where only the fearless can wear the shirt". One more Bayern goal would tilt the scales via the away goal tiebreaker. While the Bayern bosses have backed Lewandowski to come out good, it remains to be seen if the 29-year-old repays the faith with a solitary performance. Hummels got his head to a corner kick, but he couldn't steer his chance on frame, sending it wide of the post and giving Real Madrid a chance to kill off precious seconds.
Should Real Madrid win on Tuesday, they will advance to their third straight Champions League final.
The victor of Tuesday's match advances to the final to face either Italian Serie A club AS Roma, or English Premier League traditional powerhouse Liverpool - with Liverpool appearing the more likely opponent as the Reds carry a 5-2 aggregate lead into their semifinal second-leg match on Wednesday.