Title has the question. I have heard that late 19th century and early 20th century graft, in many local and state governments was widespread and have found many works on metropolitan administrations, such as Tammany Hall and Chicago Mayor Daley, Sr., but what about our Chief Executive office?
This is not my field, but the first thing that comes to mind is the extremely contentious election of 1876, when Hayes, a Republican beat Tilden, a Democrat. Tilden won the popular vote and led the electoral college by 19 votes with 20 votes disputed. In three states, both parties claimed victory, and in a fourth, one elector was illegal. So a committee was created to figure out what to do with those 20 votes.
The initial committee had 7 Republicans and 7 Democrats, and was led by 1 independent (a Supreme Court Justice). The Democrats of Illinois tried to buy his vote by electing him to the Senate, but instead he resigned from the committee, forcing them to choose another leader from the Supreme Court. All of the rest of the Justices (4 were already on the committee) were Republicans. So Republicans now had a guaranteed 8-7 majority. Not coincidentally, by several 8-7 votes (one for each state in dispute), all 20 electoral votes were delivered to Hayes, giving the Republicans a 1 vote electoral college victory.
Democrats went along with this because of the informal compromise of 1877, where Hayes effectively ended reconstruction.
For more under-the-table vote rigging, I don't know about historical consensus, but Kennedy's victory hinged on Illinois, and it's at least a common theory that the votes from Chicago under the Daley machine were rigged heavily in his favor to help him win.
So, in the latter case, it's still municipal fraud that possibly affected the national election, and in the former, it's clear procedural chicanery that was out in the open.