Whenever Ringo Starr is asked about the pianist/organist, singer and “fifth Beatle” Billy Preston, “He never put his hands in the wrong place” is his highest compliment.

One music producer who worked with the two-time Grammy winner marveled at Preston’s ability to “play any song” by just jumping in, “anticipating” correctly every note that needed to come next.

And musicians far and wide sang his praises over his sense of melody, rhythm and timing.

A glorious new documentary about the Gospel, soul, pop and funk singer who toured with the Stones and played with Ray Charles, Aretha Franklin, Little Richard, Neil Diamond and Johnny Cash among others also benefits from great timing.

“Billy Preston: That’s the Way God Planned It” is making the festival rounds hot on the heels of the critically acclaimed “Saturday Night,” a movie documenting the hours leading up to the 1975 premiere of “Saturday Night Live.”

Whatever else that movie has going for it, casting Jon Batiste as Preston, the first-ever musical guest on the show, proves as fortuitous as flying Preston and his band to New York to do “NBC’s Saturday Night” was nearly 50 years ago. Batiste’s Preston steals the picture, providing an electric third act lift much as Preston lifted that premiere episode of what became a long-running series.

And that film came not that long after Peter Jackson’s heralded “Get Back” documentary, which remembered The Beatles’ embattled final LP and final live “rooftop” performance, “rescued” by the infectiously upbeat musical genius Billy Preston.

But as Emmy-winning TV director Paris Barclay’s lively and moving new documentary reminds us, Preston’s was a troubled life of triumphs that began before he was in middle school, and tragedies tied to that early fame.

Preston kept his sexuality hidden for most of his life, but was unable to keep his addictions, financial and legal troubles out of the press. He is remembered for that million-watt smile, but intimates tell of his love of Courvoisier and weakness for crack cocaine.

And the fact that he’d talk about Gospel music training, his early encounters and work with Ray Charles and Nat King Cole, but not about touring with Little Richard in his early teens speaks of secrets he carried to his grave.

Barclay interviewed a Who’s Who of musical luminaries, family members, longtime friends and music insiders for “That’s the Way God Planned It,” which takes its title from an early (minor) hit composition Preston put out on the Beatles’ Apple Music.

Generous samples of Preston’s filmed performances turn up, reminding us of the L.A. Gospel keyboard prodigy cast to play the young W.C. Handy in 1958’s “St. Louis Blues,” which led to an early TV appearance with the film’s star, Nat ‘King’ Cole.

At his peak, Preston was the greatest “side man” ever, the fellow who “stole” every recording session and ensemble performance he turned up in, according to his longtime friend and collaborator Eric Clapton. That’s because Preston was “always the best musician in the room,” a producer reminds us.

Hit singles? Did you remember he wrote “You Are So Beautiful,” the instrumental “Outa Space,” “Nothing from Nothing” and “Will It Go Round in Circles?”

His admiring collaborators speak of the effortlessness with which many of his songs were conjured, and Clapton and Starr and others recall how he’d show up at the studio, start picking around the melody and make song after song by some of the icons of his musical era better.

Family members, friends and colleagues talk of the sexuality Preston kept hidden, and singer, actor and gay fashion icon Billy Porter provides context for why that was and how tragic that could be.

Probably molested as a child, Preston in turn faced arrest on that charge much later in life, and “boys” and attractive young men were often in his company but “never talked about.”

Being the “Fifth Beatle” made him lifelong friends with George Harrison, and a key member of the “Concert for Bangladesh” band assembled for that landmark benefit show in 1971. But Preston’s big shot at the permanent A-list was his title-role turn in the misguided film of “Sgt. Pepper’s Lonely Hearts Club Band,” in which Preston’s sparkling presence arrives too late to save one of the all-time box office flops.

The opening sequences of “That’s the Way God Planned It” will leave the casual music and modern music history fan slack-jawed in awe at Preston’s gifts and the places he showed them off. And the latter acts will move many, as he faced his demons and prison time, with true friends coming to his aid but never filling the void that loneliness, closested isolation and addiction created.

Barclay shows a sure hand at knowing where the fun in his subject is — Mick Jagger learning to tone down his mockery of Preston’s collection of oversized Afro wigs — as well as where the tragedies lie. And he makes sure this most-satisfying biography of the Rock and Roll Hall of Fame member ends on a high note, Preston’s late-life appearance at the Concert for George.

Even in that star-studded event, event-organizer Clapton grouses with a smile, the man at the Hammond B-3 stole the show and “the song I wanted to do.”

Cast: Billy Preston, Ringo Starr, Merry Clayton, Mick Jagger, Olivia Harrison, Rev. Sandra Couch, Billy Porter, Sam Moore and Eric Clapton.

Credits: Directed by Paris Barclay, scripted by Paris Barclay and Cheo Hodari Coker. A White Horse Pictures release.

Running time: 1:44