Final answer:
During the Fourth Party System, the Republican Party was the dominant force in American politics, maintaining control over the presidency with the exception of Democrat Woodrow Wilson's two terms.
Step-by-step explanation:
The dominant political party during the Fourth Party System was the Republican Party. This era of American politics is characterized by the Republicans' control over the presidency, with the notable exception of Democrat Woodrow Wilson, who was elected in 1912 and 1916. Populist and Progressive movements did pose challenges to the major parties, but the Republicans maintained their dominance during this period.
Throughout this time, the Democratic Party saw occasional success but was largely overshadowed by the Republican influence on national politics. This phase marked a significant era in American political history and featured key issues such as economic reform and government regulation, which were focal points for the Progressive movement and shaped the country's political discourse.