The world champion sealed top spot as the only undefeated team in Group F after a pulsating encounter in Budapest, where a pair of Cristiano Ronaldo penalties saw the five-time Ballon d'Or winner draw level with Ali Daei as the leading international goalscorer of all time on 109.
Benzema's lengthy exile from France duty means he is nowhere near such dizzying individual numbers, but he levelled from the spot before half-time at the Puskas Arena.
That was goal 28 for Les Bleus, coming almost six years after 27 arrived as part of a double in an October 2015 friendly against Armenia.
The wait for number 29 was nowhere near as long as he latched on to Paul Pobga's sumptuous throughball two minutes into the second half.
"There is a lot of joy, pride, I think everyone was waiting for it," he said.
"There was this pressure on me from all over the country. But I'm a football player, I'm a professional, I need that pressure too.
"So it's nice to score and to be qualified. For my club, I'm used to scoring, but I wanted to score in this team because I know that goals are very important in this competition."
Benzema's goals meant France secured a comparatively favourable last-16 tie against Switzerland, with Portugal having to face the world's number-one rated side Belgium and Germany – who flirted with disaster in a 2-2 draw with Hungary – pouching a Wembley date versus England.
"It was a big game against a great nation. We know Portugal, [they have] a lot of intensity. There were goals and opportunities," the Real Madrid striker said.
"We tried to play, to get chances and we managed to score two goals.
"There is all the pressure around me, which is normal but you should never give up. This is what I do, trying to make movements and today it smiled on me but the most important is that we are qualified."
Benzema said: "These are not doubts, but I feel such an expectation from the whole country, which is normal for me after five years of waiting. I will savour it with everyone.
"This is what we need to go to the end. Personally, it warmed my heart and I hope there will be other evenings like this."