Deduno (6-3) didn't allow a hit until the sixth inning, ultimately controlling the Indians on three hits and three walks while yielding two runs.
The right-hander struck out six as the Twins won took three wins in their four-game series against the Tribe.
Florimon tripled and scored the go-ahead run on Ben Revere's sixth-inning single, then chased home Matt Carson with a double in the next frame, putting the Twins up 4-2.
Cleveland's Justin Masterson (11-13) was touched for six runs on seven hits over 6 2/3 innings.
Lonnie Chisenhall homered for the Indians.
Celebrity Families of 2014 [PHOTOS]