Kate Hudson, center, and Jong-seo Jun, right, in Mona Lisa and the Blood Moon (Saban Films)

Ana Lily Amirpour’s last feature, The Bad Batch, hid its warm, beating heart beneath a post-apocalyptic, bloody, and ironic surface. Her latest offering, set in a scuzzy, neon-drenched New Orleans, wears its heart on its sleeve.

The story begins in a mental institution, where a formerly catatonic, young patient, Mona Lisa Lee (Jong-seo Jun), suddenly snaps out of it and escapes, using a low-key form of telekinesis where she can control the person who is looking at her. She then wanders toward a convenience store and runs into Fuzz (Ed Skerin), who looks like he’s on loan from Harmony Korine’s Spring Breakers, outrageously decked out in hip-hop threads. He takes a shine to her and lures her into his car. Our guard is up as Mona Lisa seems, at this point, incapable of quite understanding the situation she may in. Turns out Fuzz is a sweet, gentle, concerned drug dealer. Eventually Mona Lisa hooks up with Bonnie (Kate Hudson), the veritable stripper with a heart of gold. She also takes a shine to Bonnie’s 11-year-old son, Charlie (Evan Whitten). All the while, she is pursued by a detective, Harold (Craig Robinson), who is having a terrible, horrible, no good, very bad day.

What Amirpour has given us is a valentine to the downtrodden. It’s like a Tom Waits tune covered by Duran Duran. Her bottom feeders strive for something better and struggle not to lose their souls or their dreams in the process. Because Amirpour doesn’t do realism in any sense, the movie’s never depressing and doesn’t quite stick to one genre. Is it a superhero movie. Kind of. But Mona Lisa is about the lowest key superhero you will ever see. Is it a road-trip movie? Well, kind of. But we essentially get a road movie that never leaves New Orleans. Is it a comedy? Some of it is very, very funny, but you never quite shake off the characters’ desperation. Nevertheless, Mona Lisa and the Blood Moon is vastly entertaining and deeply moving.

Mona Lisa is a cipher, a young woman who was committed when she was 10, and she has no idea why she has these unusual powers, but instinctively uses them on bullies and, like Batman, doesn’t kill anyone. She just wants them to learn their lesson. Jun manages a mixture of childish innocence and curiosity with the undercurrent of a feral cat. Her head is always cocked to one side, in a state of wonder and bemusement.

The most developed character is Bonnie, the down-and-out, fast-talking, fast thinking stripper who takes Mona Lisa under her wing. Her empathy for Mona Lisa is real, but once she realizes Mona Lisa’s powers, she takes full advantage. Yet Amirpour does not judge her in the least. Bonnie is a poor stripper with a kid and, as far as she is concerned, Mona Lisa may be their ticket out of a pretty sad life. Hudson, in one of her best roles in years, tears into the part, speed-talking in a Queens accent, like Marisa Tomei in My Cousin Vinny. Bonnie is acutely aware that she is usually the smartest person in the room (which is no great shakes, considering the rooms she ends up in), and she plays up her physical beauty to obfuscate her intelligence.

Whitten scores as Bonnie’s son, who wanders the neighborhood at night while his mom works, and there he forms a bond with Mona Lisa. As the film’s moral center, Charlie actively searches for the right thing to do amid an absent mom and neighborhood bullies. Robinson, usually known for his comedic roles, is the cop who becomes inordinately obsessed with tracking Mona Lisa down after her escape from the institution. And then there is Skrein. His Fuzz represents the soul of New Orleans: gaudy, flashy, just a bit skeezy, but also empathetic, caring, and laid-back enough that nothing fazes him.

With Mona Lisa and the Blood Moon, Ana Lily Amirpour has made great strides as a filmmaker, and she was pretty darn good to begin with. But here she has created a smart, sweet, funny film about making connections and tearing down emotional walls without giving up her hipster sense of cool. She has just added depth to it. It’s a delight.