If there’s one thing successful innovators have shown over the years, it’s that great ideas come from unexpected places. Who could have predicted that bicycle mechanics would develop the airplane or that the US Department of Defense would give rise to a freewheeling communications platform like the Internet?

Senior executives looking for ideas about how to make their companies more innovative can also seek inspiration in surprising sources. Exhibit One: Brad Bird, Pixar’s two-time Oscar-winning director. Bird’s hands-on approach to fostering creativity among animators holds powerful lessons for any executive hoping to nurture innovation in teams and organizations.

Bird joined Pixar in 2000, when the company was riding high following its release of the world’s first computer-animated feature film, Toy Story, and the subsequent hits A Bug’s Life and Toy Story 2. Concerned about complacency, senior executives Steve Jobs, Ed Catmull, and John Lasseter asked Bird, whose body of work included The Iron Giant and The Simpsons, to join the company and shake things up. The veteran of Walt Disney, Warner Brothers, and FOX delivered—winning Academy Awards (best animated feature) for two groundbreaking movies, The Incredibles and Ratatouille.

Ten days before Ratatouille won its Oscar, we...