This popular vote for United States Senator was technically only an advisory vote as the 17th Amendment had not yet been adopted, although the amendment had already been passed by Congress and ratified by Minnesota earlier in 1912. In accordance with the 1912 vote, the Minnesota Legislature unanimously elected Knute Nelson on January 21-22, 1913 for the term beginning March 4, 1913.
Source for Popular Vote data: Minnesota Secretary of State. The Legislative Manual of the State of Minnesota 1913, Minnesota Secretary of State (https://babel.hathitrust.org/cgi/pt?id=uiug.30112001794970&view=1up&seq=532) (accessed 25 Oct 2023)