The movie took best film as well as best director for Jenkins and best screenplay, cinematography and editing.
Starring Mahershala Ali and Naomie Harris, Barry Jenkins's movie tells the life story of a young African American struggling to find his place as he grows up in a rough neighborhood of Miami.
The movie -- made for just $1.5 million -- took best film as well as best director for Jenkins and best screenplay, cinematography and editing.
"This one is tough. There are so many amazing directors in the category," said Jenkins, who beat Andrea Arnold ("American Honey"), Pablo Larrain ("Jackie"), Jeff Nichols ("Loving") and Kelly Reichardt ("Certain Women") to the prestigious directing award.
Backstage, the 37-year-old said "Moonlight" was meant to be a symbol of inclusivity at a time when he was angry about how divided America had become during and after the presidential election campaign.
Best actor went to Casey Affleck, 41, whose acclaimed performance about a loner who must confront his dark past in "Manchester by the Sea" has seen him win numerous awards.
"The policies of this administration are abhorrent and will not last. They are un-American," he said on a night of speeches marked by ridicule of or contempt for Republican President Donald Trump.
Best actress went to Isabelle Huppert, the French star of Paul Verhoeven's rape-revenge drama "Elle" who is tipped to mount the most serious challenge to runaway favorite Emma Stone ("La La Land") at Sunday's Oscars.
"It's independence that makes art win," the French actress said in her acceptance speech, later adding backstage: "You can rebel through art. That's what I like about art."
Best supporting actor went to Ben Foster for David Mackenzie's neo-Western "Hell or High Water" while Molly Shannon won the supporting actress prize for playing a mother with cancer in Chris Kelly's comedy drama "Other People."
After a patchy few years, the Film Independent Spirit Awards has become a reliable indicator of independent movies that will be in the running at the Oscars.
Four of the last five "best feature" winners at the event in Santa Monica have gone on to win the best film Oscar the following day.
"Moonlight" is competing at the 89th Oscars with Damien Chazelle's awards season darling "La La Land," however, and is likely to become one of the exceptions.
"Moonlight" has swept a string of honors ahead of the Oscars, including best drama film at the Golden Globes and top prizes from the Screen Actors Guild and the Writers Guild of America.
It was nominated for and won six Spirit Awards. It surprisingly did not earn nods in the individual acting categories, despite Harris and Ali being Oscar contenders.
The entire cast, Jenkins and casting director Yesi Ramirez however got the special Robert Altman achievement award.
One disappointment was "American Honey," written and directed by Arnold and starring Shia LaBoeuf, which also secured six nominations, but walked away empty-handed.
"Jackie," Larrain's political drama focusing on former US president John F. Kennedy's assassination through the eyes of First Lady Jacqueline Bouvier Kennedy, also won nothing.
It had nominations for directing, editing and best feature, as well as a nod for Natalie Portman's intense, committed performance in the title role.
Kenneth Lonergan's New England-based family drama "Manchester by the Sea" went into the afternoon with five nominations but ended up going home only with Affleck's win.
The movie, which opened to some of the best reviews of the year, is up for best film and best actor and supporting actor and actress at the Oscars.