Underdog candidates like Harry S. Truman in 1948 and Barack Obama in the 2008 primary contest struck many voters as authentic leaders who were willing to speak truth to power (Truman railing against a “do-nothing Congress,” Mr. Obama opposing the American invasion of Iraq) and who did not try to be all things to all voters. Truman was quintessentially Midwestern and didn’t shy away from his roots, no matter what coastal elites thought of him. Mr. Obama was the first black presidential nominee and didn’t shy away from his race, giving an eloquent speech in the face of controversy over his Chicago pastor. Many Americans came to see both men as the real deal.

“Underdogs succeed when the voters are in a certain zone — I call it ‘the voter zone’ — where they are looking for something, and the underdog candidate taps into that something,” said Tad Devine, a veteran Democratic consultant who is advising Mr. Sanders. “It can be a set of issues, attitudes or beliefs that voters feel are being overlooked by the front-running candidates. If the underdog can get into the voter zone with the voters by themselves, and if they are credible, they can win despite the odds.”

Both “Fun Home” and “An American in Paris” had plenty of credibility in the run-up to the Tony Awards: They were winning over critics and filling seats with paying customers, two meaningful measures in the eyes of the 844 Tony voters eligible to cast ballots for best musical. But “Fun Home” had a freshness that appealed to many liberals among the Tony electorate: Shows about lesbians are rare on Broadway. Its producers, meanwhile, had shown perseverance by developing the musical for years and raising enough money ($5.2 million) to transfer it from the Public Theater, Off Broadway, to Broadway.

And unlike the beautiful people and plot contrivances of “An American in Paris,” the relationships and emotions in “Fun Home” felt deeply authentic: a family of normal-looking people where love and loyalty mixed with resentments and rancor. (Come to think of it, the father’s bad haircut brings to mind Mr. Sanders’s messy mop.)

“A lot of people loved ‘Fun Home,’ but they also believed in what it was about and wanted to see it win,” said Scott Sanders, a veteran Broadway producer (who is not related to the senator).