You almost won’t recognize Steve Coogan and John C. Reilly in this delightful homage to Laurel and Hardy

“Stan & Ollie,” a generous, warmhearted film about the comic duo of Stan Laurel and Oliver Hardy, begins on a graceful, amusingly self-referential note. The film opens in 1937, in a dressing room where the team prepares for their next scene together, trading anecdotes about ex-wives, alimony woes, Oliver’s latest gambling trip to Tijuana and the mundane details of salaries and contracts.

From there, the camera follows the two through a studio back lot to a busy soundstage, an exercise in high technique that not only proves director Jon S. Baird’s bona fides as a stylist, but also reveals important information about the characters: It’s clear that Oliver, who goes by the nickname “Babe” to friends and loved ones, has a problem with women and wagers whereas Stan has his far more practical eye fixed firmly on the bottom line. Even more to the point, the tracking shot through the Hollywood dream factory is a brief but utterly transporting tribute to the movie magic that “Stan & Ollie” celebrates as joyously as its mismatched but perfectly paired heroes.

After that delightful prologue, “Stan & Ollie” begins in earnest – 16 years later, by which time Laurel and Hardy – now competing with television, their own reruns and a couple of imitators named Abbott and Costello – have been forced to tour second-tier theaters in Britain, staying in un-grand hotels and playing to half-empty houses. They’re not happy about it, but they’re troupers above all else, playing their classic “bits” as if they’re discovering them for the first time.

Written with compassion and worshipful wit by Jeff Pope, “Stan & Ollie” pays tribute to a bygone era when a little song, a little dance, a dollop of slapstick and some clever stage patter counted as enormously successful pop entertainment. By dint of sheer self-preservation and professionalism, Stan and Ollie manage to turn their final tour together into a triumph, not knowing that it’s a curtain call, not just for their nearly 30-year partnership but for an entire culture.

As a winsome glance back, and as a piece of artistic preservation, “Stan & Ollie” would be enjoyable enough. But it becomes truly transcendent in the hands of John C. Reilly and Steve Coogan, who play Ollie and Stan with intelligence and spirit that go beyond their own uncanny physical performances. Reilly is particularly memorable as he slips effortlessly into the rotund Hardy’s improbable teacup-pinkie grace.

Happily, “Stan & Ollie” calls on Reilly to sing once or twice, his crystal-clear tenor lending “Shine On, Harvest Moon” the gentle nobility of a hymn. The role of Stan Laurel is less showy, and all the more difficult for that. Coogan, known for edgy characters who exist just this side of nastiness, here submerges his snarkiest instincts to deliver one of the most sincere and touching portrayals of his career.

“Stan & Ollie” rumbles along as a delightful two-hander, with the filmmakers allowing Laurel and Hardy’s most famous routines to play out in their entirety, like fine dance sequences. They’re also folded into the body of the film itself, such as when a valise goes skittering down a flight of stairs at a train station. But things heat up – in terms of comedy and high drama – when the wives show up. As Lucille Hardy and Ida Laurel, Shirley Henderson and Nina Arianda prove to be just as tetchy and hilariously funny as the men they ferociously protect at every turn.

Residual tension – echoes of a brief period when the two split up – animates “Stan & Ollie.” At one point, old betrayals and rivalries boil over, and Baird stages one pivotal confrontation while a Beatlesesque group plays in the background, suggesting that the petty problems and resentments of a couple of vaudeville pros will soon be atomized into irrelevance by the coming pop invasion.

The arguments, when they arise, are regrettably on-the-nose and spelled out. But by that time, “Stan & Ollie” – working through Reilly and Coogan’s superb physical and emotional work – has allowed viewers to understand what made their characters so great, and so beloved, in a film that magnanimously invites us into a world no less recognizable for being almost entirely erased.

“Beautiful madness,” one observer calls Laurel and Hardy’s art. “Stuff and nonsense,” opines another. “That’s entertainment,” this humane, thoughtfully crafted film reminds us. And, as it’s ever been, entertainment is all in the timing.