No doubt about it — Sherlock Holmes is the sleuth of the century.

On the silver screen, Robert Downey Jr. plays the private investigator as a Victorian James Bond — brash, brilliant and surprisingly comfortable with fisticuffs.

BBC America’s “Sherlock” stars Benedict Cumberbatch as a cold, clinical technophile in 21st-century London, while “Elementary,” which premiered in September on CBS, finds Sherlock (Jonny Lee Miller) solving crimes in present-day New York City with the help of his surgeon-turned-sober companion, Joan Watson (Lucy Liu).

“Sheer-Luck Holmes,” now playing at the Great American Melodrama in Oceano, is the latest production to bring the Great Detective to life. Unlike its peers, however, this musical spoof mines Arthur Conan Doyle’s stories for laughs as well as dramatic tension.

Directed and choreographed by Eric Hoit, “Sheer-Luck Holmes” establishes its silly yet thrilling tone in its first scene, set at London’s Royal Museum circa 1894.

Museum curator Sir George Blackstone (Billy Breed) has just deciphered the inscription on an ancient Egyptian bust of Anubis, granting him access to untold riches. No sooner has he shared his discovery with Professor Plum (Alex Sheets), however, than he collapses — presumably struck dead by the curse that guards the pharaoh’s treasure.

Sir George’s corpse is discovered by assistant curator Adam Nevilton (Steven Freitas) and his fiancé, Eve Blakenship (Crystal Davidson), who summon Sir George’s personal physician, Dr. John Watson (DJ Canaday).

Not surprisingly, detective Sherlock Holmes (Philip David Black) is hot on Watson’s heels.

He quickly deduces that Sir George was poisoned — but by whom?

Did Plum or his cohort, Colonel Mustard (Sheets again) have something to do with the curator’s death?

A visit to Sir George’s palatial home turns up a few more suspects: Sir George’s brother, Lord Edmund Blackstone (Breed again), his ward, Gwendolyn Periwinkle (Bethany Rowe), and her gassy, kleptomaniac caretaker, Nanny Gooseberry (Jacqueline Hildebrand).

Watson quickly falls for oddball beauty Gwendolyn, but she’s literally under the spell of Lord Blackstone. He plans to steal the treasure himself, provided he can get that pesky detective out of the way.

As Holmes would say, “The game is afoot!”

A zippy, zany comedy, “Sheer-Luck Holmes” is at once an affectionate sendup of Sherlock Holmes stories, and a tribute to their staying power.

Ben E. Millet’s script, adapted from “Holmes & Watson” by Peter Van Slyke, is stuffed with puns, physical comedy and pop culture references to everything from Charlie Sheen to the board game “Clue.” The musical numbers, meanwhile, borrow their cues from sources such as “Camelot,” “Gentlemen Prefer Blondes” and “Oliver!”

No wonder the cast looks like it’s having fun.

Black is suitably superior as Sherlock, while Breed clearly relishes his role as the fiendish Lord Blackstone. When he launches into a villainous parody of Michael Jackson’s “Thriller,” it’s impossible not to chuckle.

Rowe, for her part, consistently steals the show as a deliciously dizzy ingénue. Just wait until you see her impression of a grunting sumo wrestler!

Performances of “Sheer-Luck Homes” are followed by “A Salute to the Film Musical,” a tuneful tribute to the song-and-dance extravaganzas of yesteryear that opens with “Hooray for Hollywood.”