Will Jevon as Helga Tboring in the Hasty Pudding’s “Heist, Heist, Baby!” (Photo: Jay Connor)

It’s Manhattan in 1992, and the rich and famous are at a gallery opening for mysterious celebrity artist Spansky when his brand-new $175 million masterpiece goes missing. This is the relatively simple premise of “Heist, Heist, Baby!,” but the show – a raucous, laugh-aloud-funny two-hour extravaganza of singing, dancing and dirty jokes – is anything but.

“Heist, Heist, Baby!” is the Hasty Pudding Theatricals’ 175th show. A Harvard group founded in 1844, the Hasty Pudding is the third-oldest theater company in the world, and has presented an original comedy musical every year since 1844, the only exceptions being for World Wars I and II and the Covid pandemic.

Alums of the Pudding include William Randolph Hearst, Franklin Delano Roosevelt and Jack Lemmon – the shows were men-only until 2018. (When Amy Poehler was awarded Woman of the Year in 2015, she said, “I want to say that it’s unsettling that there will be no women on stage tonight,” she said. “You know it’s time for a change when the Augusta National Golf Club has lapped you in terms of being progressive.”)

As a result, men in drag has been the norm since the beginning; the Puddings call their annual show a “no-holds-barred burlesque.” There’s still some of that, and while there was some fine queening on the stage, including people of all genders is an overdue and welcome change that added monumentally to the show.

The play opens on aspiring journalist Rita L’Boutette (Isabella Peña), who comes to the city from a small town and sneaks into the museum looking for a story she hopes will be her big break. Her opening number, “Off the Record,” was particularly good, with lines including “Call me Rupert Murdoch ’cause I’m gonna break the news!” setting the tone for what would be a funny, clever and culturally relevant show – Pudding plays are always meant as social and political satire. The cast of characters includes Alec Zis (Sophie Garrigus), who’s hosting the event at the museum, and a list of VIPs that includes wealthy geriatric Cassius Whatimafter (Alexander Lim) and his gold-digging young wife Eileen Onyoufinancially (Matthew Cole), teenage pop star Holden Outhopeforyou-Girl (Kaylor Toronto) and suspiciously old fourth-grader Eli Zaboutizage (Bernardo de Moura Sequeira).

When the Spansky painting goes missing during a moment of darkness, the crew goes on a long, winding mission to figure out the identity of the thief; when Cassius is killed at the end of Act I, they’re faced with a second mystery. Rita is desperate for the scoop, and Mel O’Dramatic (Emma Rogers) and Mischa Nimpossible (Isabel Wilson) are under pressure to carry out their heist mission for an unknown boss. Other characters include down-on-his-luck paleontologist Arthur Bonesburiedhere (Nikita Nair), who spends much of the play looking for a missing bone and accidentally releases ghost queen Helga Tboring (Will Jevon, a particularly good ghost), who’s been stuck in a piccolo after Beelzebub banished her there from hell.

Clearly it’s all a bit ridiculous, but that’s part of the fun. It’s an easy enough plot to follow, interspersed with some really solid songs. Written by juniors Maddie Dowd and Sophie Garrigus, “Heist, Heist, Baby!” is profoundly clever and well-paced. The punny names alone, like Rita L’Boutette (“read all about it”), Cassius Whatimafter (“cash is what I’m after”), Eileen Onyoufinancially (“I lean on you financially”), Arthur Bonesburiedhere (“are there bones buried here?”) and Helga Tboring (“hell got boring”), were enough to leave me feeling confident that Dowd and Garrigus, who also starred as Alec, could have real futures in comedy. I didn’t find much of a deeper meaning in the play. I didn’t feel like I needed to.

The acting was convincing and the singing was impressive; the scenes and numbers featuring most or all of the 10-person cast were some of the best. Arthur and Eileen’s voices were especially captivating, and though he didn’t really sing until Act II, “Holden Out Hope For a Hero” was Toronto at his best. The settings, costumes and a top-notch pit band added to my sense that this production was as good as, if not better than, the professional theater offerings in Cambridge and Somerville. The play did have a college-kid kind of sensibility, with lines such as “How can you possibly focus on electricity when my butt is right here?” and “Our story’s at a climax, one I’d never fake!” (and there was some Harvard-specific fodder: “I’m feeling as low as IQs are at Yale”), but that was about the only thing reminding me I was watching a group of 20-year-olds.

The Pudding is probably best known for its Man and Woman of the Year Awards, presented annually to performers – this year, to Barry Keoghan and Annette Bening – who have made an impact on the world of entertainment. Its annual show is not to be overlooked, though.

There are two chances each on Saturday and Sunday to catch the show in Farkas Hall before before the cast embarks on New York and Bermuda runs. Then it’s a long wait until the 176th production, likely also to be an extremely smart, funny play worth the night out even if you’re not attending Harvard College.

• At Harvard University’s Farkas Hall Studio, 10-12 Holyoke St., Harvard Square, Cambridge.