Randall Wallace’s big-boned tale of the horse that won the triple crown in 1973—and the people who gave him the chance to do so—can be taken as a sort of companion piece to 2003’s “Seabiscuit.” Like that picture, it aims to uplift by showing us the indomitable spirit—both human and equine—that resulted in such a triumph. And like it, the result is calculated and manipulative. But it does its job skillfully, although it moves a lot more slowly in the expository material than it does in the race sequences.

The difference is that the “Rocky” element of the story doesn’t apply to the horse, which is clearly a champion-in-the-making from the moment of its birth, but to its owner, Penny Tweedy (nee Chenery) (Diane Lane), the Denver housewife who takes charge of the family’s floundering Virginia ranch when her mother dies, leaving her infirm, beloved father (Scott Glenn) and a brother (Dylan Baker), a Harvard professor of Economics who wants to sell the place to cover the anticipated estate taxes. But Penny, her father’s daughter, is determined to save the place, especially after a coin toss with rich rival Ogden Phipps (James Cromwell) gives her the colt that will eventually become Secretariat—the horse she believes with the right trainer and jockey will be a champ.

So against all the odds Penny leaves her Denver family, including grumpily practical husband Jack (Dylan Walsh) and four children, largely in limbo while she induces sartorially flamboyant Lucien Laurin (John Malkovich) to return from retirement to take over as the horse’s trainer, and eventually takes on hard-driving Ronnie Turcotte (Otto Thorwarth) as their rider (as well as long-time family employee Eddie Sweat, played by Nelsan Ellis, as groom). Together they struggle through financial setbacks, personal dilemmas and some horsy physical problems to reach their remarkable success against voluble rival breeder Poncho (Nestor Serrano).

“Seabiscuit” situated its story within the larger historical context of its time, with the tale of the little horse that could used not just as a reflection of the triumph of its human characters against enormous odds, but the pluckiness of the whole country facing the crisis of the Great Depression. When “Secretariat” tries something similar—periodically inserting scenes of the older Tweedy daughter (AJ Michalka) as a Vietnam war protestor—it goes lame.

But on the more intimate scale, the picture works well enough, even though the occasional moment of anthropomorphizing the horse come off as faintly ridiculous, and some of the sequences involving humans go way too far in the rah-rah department. (Ellis’ big scene, in which Sweat addresses the early-morning racetrack before the Kentucky Derby, is positively embarrassing.) Nor does Lane bring much to her role beyond an attitude of steely determination that makes her resemble a young Glenn Close.

But Wallace and scripter Mike Rich have wisely surrounded her with a supporting cast that add color to the proceedings. First among them is Malkovich, who clearly relishes channeling Laurin’s eccentricity and larger-than-life persona, but also brings to the part a degree of trepidation and vulnerability. Thorwarth, a real jockey making his acting debut, is hardly of Olivier quality, but is more than adequate. Glenn cuts a sympathetic figure as Penny’s ailing father, and even more engaging are Margo Martindale as his loyal secretary, Fred Dalton Thompson as his long-time lawyer, and Cromwell as his equally long-time rival. Less impressive are Walsh and Baker, in what are essentially thankless roles; Ellis, who frankly comes across as very old-fashioned as the drawling groom; and Serrano, as the pompous owner of Secretariat’s chief rival.

The movie is bathed in a burnished, Hallmark Hall of Fame glow by cinematographer Dean Semler, who points up the period detail in Tom Sander’s production design, Naaman Marshall’s art direction, Patrick Cassidy’s set decoration and Michael T. Boyd and Julie Weiss’s costumes with the degree of italicization one would expect in such a style. But he and editor John Wright really come into their own in the race sequences, portions of them from the rider’s perspective, which capture the excitement of the come-from-behind victories that Secretariat specialized in until he chose to go all out and blow out the competition in the final race. Unfortunately, Nick Gennie-Smith’s score is a generic example of uplifting puffery; a lot fewer swooping violins and throbbing brasses would have been preferable.

“Secretariat” is an unabashed crowd-pleaser of the old school, with a dash of feminist triumph added to the sports mix to make it more palatable to contemporary taste. It’s a purely popular piece, but that certainly will assure its accessibility to the mass audience at which it’s aimed.