The one that always comes to mind for me did not do it subtly, but is incredibly satisfying to watch unfold.
Samurai Flamenco is about a dude who grew up idolizing TV superheroes and now works as a successful model but moonlights as a true-to-form pure-of-heart superhero in the middle of an utterly normal and realistic Tokyo. A large portion of the initial story is about him and those close to him deaingl with him being a superhero in a world that doesn't really fit the model of TV superhero that he is. It's a pretty compelling story about the value of your childhood dreams and also what it means to understand the world for what it is, and how you can slowly make it more into what you imagined it would be.
And then, without warning, seven episodes in a sentient gorilla with a guillotine built into its torso shows up and just kills a bunch of people. And a legitimate super villain unleashes actual super-powered monsters on the city. And suddenly the entire show pivots. These things actually do exist.
I won't spoil too much but the show continues to evolve: it doesn't just stop at a superhero vs. super-villain storyline. It continues to escalate and shift in its level of fantasy. By the end it even neatly (if strangely) explains why the world was perfectly normal up until the exact moment it wasn't.
It's a great show and not too long either.
Murakami does this all the time but it still works.
My favorite "portal" is the ladder up onto the freeway section. It's so in keeping with how I imagined reality when I was a child and still do in dreams.
Yeah Murakami's transitions between utterly mundane and fantastical are excellent. I also love that his stories will drift heavily into the fantastical and then just as easily drift back in that way that makes you ask what actually happened.
For those looking where to start with Murakami, I think a great entryway is Wild Sheep Chase. It isn't too long and showcases his style brilliantly.
Beyond that there's Wind Up Bird Chonicle (a truly excellent book but pretty gigantic read) and Colorless Tsukuru Tazaki (my personal favorite but only with passing fantastical elements)