Harry Potter’s voice has changed.

That’s not just because actor Daniel Radcliffe turned 14 during the filming of “Harry Potter and the Prisoner of Azkaban.” Conceptually, the third picture in the series also has undergone a transformation that makes the project deeper and more resonant.

The latest adaptation of J.K. Rowling’s beloved novels features the same principal cast, same screenwriter (Steve Kloves) and the same production studio, yet it looks and feels utterly different thanks to a new director. Gone is capable gun-for-hire Chris Columbus, with artsy Mexican filmmaker Alfonso Cuarón taking his place.

The man responsible for the sexy coming-of-age drama “Y Tu Mamá Tambien” delivers a darker, scarier and grittier effort. Those who feared the franchise might grow as stale as “Batman” or “Alien” need not worry, as Cuarón proves there is still a little magic left up Potter’s sleeve.

This is especially noteworthy considering the plot structure is nearly identical to the first two movies/books.

1. Harry is mistreated at home by his resentful relatives, who in turn get their comeuppance thanks to some supernatural incident.

2. Harry then takes a trip to Hogwart’s using a unique form of transportation.

3. He meets the new instructors, who inevitably include the latest Defense Against the Dark Arts teacher.

4. He gets sucked into a mystery that centers around him.

5. Joined by friends Ron (Rupert Grint) and Hermione (Emma Watson), he breaks rules but never REALLY gets in trouble.

6. He relies on a magic item that gives him powers beyond what the other students can muster.

7. The mystery resolves in an unexpected way, with the good guy/bad guy roles somehow reversed.

In “Prisoner of Azkaban,” Gary Oldman plays the escaped wizard of the title, who is reportedly on his way to Hogwart’s to murder Harry. Attempting to recapture the fiend are the spooky Dementors, who look like a cross between Ring Wraiths and the Ghosts of Christmas Future.

New faculty includes the pensive Prof. Lupin (David Thewlis) — those familiar with Latin may guess from what affliction he suffers — and eccentric Prof. Trelawney (Emma Thompson), a New Age witch whose divination practices include reading tea leaves.

Just follow the chart above for how all this progresses.

Credit Cuarón for being able to put his own mark on a picture so potentially formulaic. He does this by toning things down rather than amping them up.

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The look of the film is muted and somber (it was shot by “Midnight Express” cinematographer Michael Seresin). And it’s also more contemporary. For instance, the kids wear street clothes much of the time rather than their stodgy choir robes.

The special effects are superior to the rest of the series because they are so restrained. There are actually entire conversations in which no CGI gimmickry calls attention to itself in the background.

Even the inevitable Quidditch match — which has always been the least compelling aspect of the movies — is shot during a rainstorm. This gives the sequence some tension that the “game” itself doesn’t have. (On a sporting note: What’s the point of even trying to score if all you have to do is catch the little flying ball in order to win?)

All this doesn’t mean Cuarón’s debut is free of glitches.

The episodic pacing causes the story to bog down in its second act. While the threat of Oldman’s wizard Sirius Black hangs over Harry’s psyche, there is little in the way of an immediate danger to give the tale momentum.

Even Harry’s ongoing nemesis Draco Malfoy (Tom Felton) does little in this chapter. Unlike the three main kids, Malfoy has not matured as appealingly. (He has the disaffected look of someone who is straddling the fence between a skate punk and a heroin addict.) He also has only two modes in the flick: spiteful bully or scared weasel, with seemingly no transition between the behavior.

Fortunately, all is redeemed by the movie’s ending. The climactic 20 minutes of “Prisoner of Azkaban” represent a tour de force of adventure filmmaking.

A lot of movies have explored the idea of how the past and future might intersect and result in alternate realities — “The Terminator” and “Back to the Future” trilogies come to mind. “Prisoner” is so clever at manipulating this time-juggling concept that it levitates the series to another level.

The final revelation hinges on Harry comprehending his own emotional psyche rather than just slaying another computer-generated monster. It’s a scene of pure inspiration, and it’s the first moment in the “Potter” anthology that can genuinely be called “magical.”