Would you believe that the 2008 big-screen remake of Mel Brooks and Buck Henry’s fondly remembered ’60s TV spy send-up “Get Smart” is actually funny? That’s not a Maxwell Smart-style exaggeration: With Steve Carell a perfect fit as the bumbling Agent 86, this 21st-century update pays homage to all the original’s catchphrases and running gags while re-imagining the spoof as an elaborate action comedy whose budget probably exceeds that of the series’ entire five-year run.

Where the late Don Adams’ Smart was completely inept, Carell’s begins as a rather competent (though absurdly meticulous) analyst for CONTROL, the super-secret U.S. spy agency in constant battle with the lunatic evildoers of KAOS. When CONTROL headquarters is attacked and the identities of most of its agents are revealed, Max finally realizes his longstanding dream and is promoted to field agent. He’s teamed with the gorgeous Agent 99 (Anne Hathaway), a seasoned spy who’s recently undergone a complete surgical makeover. Their mission to foil the nuclear-blackmail plot of ruthless KAOS villain Siegfried (Terence Stamp) leads to a breathless series of death-defying adventures and mishaps, often spurred by Max’s ill-advised bravado.

Unlike Barbara Feldon’s incredibly patient and doting secret agent, Hathaway’s 99 doesn’t have much use for her new and painfully green partner. The two bicker throughout much of the film, but the seemingly mismatched Hathaway and Carell have so much chemistry, the actors’ mutual affection seeps through their scripted antagonism—it’s believable when they eventually bond. Just as she held her own against Meryl Streep in The Devil Wears Prada, the beautiful Hathaway proves she has the comic chops to complement the zany Carell.

Also well-cast are Alan Arkin as the eternally buffeted Chief of Control and Dwayne Johnson (aka The Rock) in the new role of Max’s idol, the smooth, macho and ultra-efficient Agent 23. Stamp, the evil General Zod in the Christopher Reeve Superman movies, brings his familiar hauteur to Siegfried, who seems to despise the world purely on aesthetic grounds, while James Caan takes some easy potshots as a very Bush-like president. Masi Oka (TV’s “Heroes”) and Nate Torrence (“Studio 60 on the Sunset Strip”) also score as easily cowed CONTROL lab nerds.

But above all, this is Carell’s film. The erstwhile 40-year-old virgin proves he’s a major comedy star, with a true gift for silly slapstick that remains grounded in a recognizably vulnerable humanity. Don Adams may have been a TV icon, but his interpretation of Max was always gag-driven and never very deep. Carell reveals the longing, frustration and insecurity of the character, in between classic comic set-pieces like his attempt to tear apart plastic handcuffs with a tiny dart gun while hiding in an airplane restroom.

Get Smart’s weakest element is its impulse to compete with the summer action blockbusters. Director Peter Segal, whose hits include 50 First Dates and Anger Management, handles the surprisingly muscular fight scenes well, but they often feel as if they’ve been grafted from a different, more generic sort of picture. Still, if Carell ever fancies himself as a more straightforward action hero, he shows he can handle that too.

Though it often strays from the casual spirit of the original, the big-screen Get Smart manages to include all the series staples, from the slamming security doors to the phone-booth elevator and cone of silence, and immortal catchphrases like “Sorry about that, Chief” and “Missed it by that much.” (And Max’s hastily improvised pseudonym, “Nudnik Shpilkes,” sounds like pure Mel Brooks.) For those who were wondering where Hymie the Robot is, a last-minute appearance offers hints of a sequel. Get Smart delivers enough laughs that the producers’ confidence is probably justified.