Prior to that year, no Democrat had ever won more than 50% of the vote in Ohio. The closest was Rutherford Hayes in 1876. Grover Cleveland won by winning in New York. In 1912, Wilson carried Ohio but only with a 40% plurality. Based on electoral history alone, there is no reason to believe that Wilson had a chance in Ohio. Had he lost Ohio, he would have lost the election.
I'm sketchy about the details, but as I understand it, the State Republican Party was engaging in a more than usually brutal faction fight. They got clobbered in the State races as well as the national one.
Wilson's position on labor relations and the like was also popular there, but I think Republican weakness was more important than Democratic strength.