If you go back and watch the 2006 Tony Predictions episode of Theater Talk, Michael Riedel stated that he didn't feel that The Drowsy Chaperone had a lot of support within the industry. On Theater Talk, Riedel predicted Jersey Boys would win, but in his column, he predicted The Drowsy Chaperone.
Because business on Broadway had been struggling for so long, it apparently used to have been a trend to vote for the big commercial juggernaut over the more ambitious work for Best Musical. Such as La Cage aux Folles winning over Sunday in the Park with George, The Phantom of the Opera winning over Into the Woods, Crazy for You winning over Falsettos, The Lion King winning over Ragtime, Thoroughly Modern Millie winning over Urinetown, Spamalot winning over The Light in the Piazzia, In the Hieghts winning over Passing Strange, Memphis winning over Fela!, etc.
But nowadays since business on Broadway has improved, the more ambitious works are winning over the big commercial juggernauts such as Once winning over Newsies, Gentleman's Guide winning over Beautiful, and Fun Home winning over An American in Paris.