The Lego Movie is a 3-D kid flick in which the entire world is apparently made of little plastic bricks (“the greatest movie ever assembled,” as the trailer wryly puts it). The description may not make your heart beat faster, but in less than two weeks it has grossed an estimated $140 million at the U.S. box office, nearing or maybe setting a record for a film released at this time of year. Considering that the movie cost only an estimated $70 million to make, and that its global prospects are extremely strong in light of Lego’s globally popular brand, the film is a major win for both Lego and the film’s producer, Warner Brothers, which (like Fortune’s parent company) is part of Time Warner (TWX).

So what’s the link to Apple? In one word, integration. Apple has conquered the world in large part because it’s the best company anywhere at integrating all the parts of the business into a knockout customer experience. Hardware, software, product aesthetics, online experience, even packaging — at Apple they’re all created simultaneously in ways that reinforce one another. Consultant Ram Charan, who leads the field in analyzing and understanding integration, explains, “Core decisions are made by integrating inputs from experts simultaneously and largely without the filters of the administrative managers of the experts.”

But doesn’t every company do that? Far from it. In fact, most large organizations find this kind of integration almost impossible. That’s why Sony (SNE) notoriously failed to defeat or even match Apple’s iPad, though it was a far larger company at the time. It couldn’t get the necessary divisions to work together, as then-CEO Howard Stringer later admitted. Steve Jobs made integration work at Apple, and he realized its importance. As he said, “Integration is the only way I could make perfect products.”

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Lego is integrating. It’s building a machine that creates an extended customer experience with its brand, in multiple media and physical spaces. This isn’t old-fashioned ancillary marketing for Lego construction toys; Lego is making money at every step. Characters and products that show up in the movie may also play roles in programs that Lego creates with Cartoon Network, in video games, at six Legoland theme parks around the world, and at 11 smaller Legoland Discovery Centers.

The company fuels this network of businesses with more than its own creations. It has proven extraordinarily persuasive in getting companies that compete with one another to license their characters to Lego. The company has toy lines featuring Batman, which is owned by DC Comics, part of Time Warner; Iron Man, which is owned by Marvel, part of Walt Disney (DIS); and Yoda and other Star Wars characters, owned by LucasFilm. They all cohabit peacefully in the Lego-verse, as it’s called. The whole system grows and prospers as one organic unit.

Integrating isn’t easy because companies naturally generate siloes as they grow. Integrators tear them down, and the results are impressive. The rest of us had better figure out how to do it in our own organizations.