How about Inception. Released a year after Avatar, and based on the amount of times it's been ripped off, the amount of times it's referenced in jokes (mostly playing on the word Inception), the amount of times I've heard it's music or sound-effects used in youtube videos, memes etc., I'm willing to say it's had more of a cultural impact than Avatar. That's just one off the top of my head.
Inception, at least as far as Sci-fi related films did strike more of a chord with certain types of people who were impressed by the plot-mechanic heavy and twisty story. But in terms of pop culture references, I don't really think it was any more referenced than Avatar was (and perhaps fewer), if it did it wasn't significantly so. One of the similar breakthroughs it had was that it was criticized for being unoriginal by South Park (Avatar was said to be based on Dances with Wolves + Smurfs; inception was Nightmare on Elmstreet), and Avatar had a Simpsons THOH episode with Bart being an Avatar of the Blue Rigelians (I assume Inception did too, but I don't recall). I have not seen much or any references to Inception since around the time it came out.
Also, I am not aware of any film that has ripped off Inception.
But you do remind me of something (and it's a counterpoint against what I have written) with another Nolan film: The Interstellar black hole probably had the biggest cultural impact of any element of an independent sci-fi in recent times. I still see it frequently. But, unfortunately as a film, Interstellar has not been well regarded... Or at least not yet.
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