Real had also sneaked through their quarter-final tie against Juventus 4-3 on aggregate, qualifying with the help of a hotly contested injury-time penalty.
Bayern, who trailed 2-1 after last week's opening leg in Germany, looked capable of inflicting this season's latest European comeback when Joshua Kimmich scored early and James Rodriguez levelled shortly after the hour.
It created enough to have made what Bayern manager Jupp Heynckes called a "blackout" by Ulreich completely irrelevant. Zidane is getting his tactics wrong, Ronaldo is getting too old, Navas is not a top-tier goalkeeper - whatever part of the team you choose to criticise, evidence supporting your case could be found this season.
"Words can not describe how disappointed I am about leaving the Champions League", the goalkeeper wrote Instagram.
"I'm delighted for him, it was exactly what he had wanted to do for so long, to score, he did it twice and gave us the possibility to go through", said Zidane. "I'm sorry. for my team and for you fans". "We still needed a third goal", he said. "We pressed up front and got the second goal".
GETTYLiverpool transfer news Jurgen Klopp is eyeing a deal for Real Madrid's Keylor Navas
He spoke to Fox Sports after helping Real to a 2-2 draw and a 4-2 aggregate success and said when asked if the ball had struck his hand: "Yes, it hit my hand". He's heard a lot recently about possible replacements to take his spot but after this game I don't think he has anything to worry about.
When quizzed on whether a penalty should have been awarded, the Brazil global added: "Well, if it hit my hand, I'd say so".
"I don't talk about referees, but it's clear that sometimes they go in your favour and other times against you, but whatever happens, you have to play football".
Benzema's two goals were also credit to Zidane, who had picked the striker despite a poor run of form that had included only one goal in 12 games.
Real, and Zidane, are now on the brink of a third consecutive Champions League triumph, and 13th overall in Europe's premier tournament.
'We're going to go there and battle for the followers, for the membership, battle with out worry and win the ultimate.
Terre Haute police officer killed in the line of duty
Indiana State Police are investigating the shooting, while Terre Haute Police are handling the original homicide investigation. That acquaintance was the suspected gunman in the earlier homicide and the suspected killer of the police officer.