I'd think the most important election was in the 20th century. 19th century Presidents really didn't have much power compared to the Congress, plus federal laws were much easier to violate back then.
OK, then I would say the 1912 election, where a fluke division of the GOP handed the election to the Democrats. In 1913 they gave us the Federal Income Tax, the Federal Reserve, and the Direct Election of senators. That's a sea change.
Except that is not the case. While amateur "historians" like to blame or praise Wilson for those three things, his election was
not the cause of any of them.
Roosevelt, Taft, and Wilson all campaigned in favor of a central bank.
All three campaigned in favor of the Sixteenth Amendment which had been sent to the states in 1909. Thirty-three states had ratified it before the nominating conventions had been held, and the needed thirty-sixth state, (Delaware, New Mexico, or Wyoming), ratified after the election, but while Taft was still in office
Direct election of Senators is even less due to Wilson, since at least with the central bank and the income tax he had a role in shaping the enabling legislation. The Senate reluctantly agreed in 1912 to send the Seventeenth Amendment to the States to forestall a Second Constitutional Convention from being called. Twenty-seven states (four short of what was needed then) had formally called for a convention to be held to propose such an amendment because of Congressional inaction, and it was widely expected that if the Senate had not caved, a Convention would have been called. Again, all three major Candidates campaigned in favor of the amendment, and while it was not ratified until Wilson had been in office a month, Wilson played only a role as one of numerous cheerleaders for its passage.
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