Daury Torrez held Lake County to one run on five hits over five innings for the win.
Carlos Penalver hit an RBI double in the second to tie the game at 1, and Kane County took a 3-1 lead on Rogers' homer in the third. Rogers added an RBI single in the fifth.
Rogers and Jeimer Candelario each finished with three hits.
Carrie Muskat is a reporter for MLB.com. She writes a blog, Muskat Ramblings, and you can follow her on Twitter @CarrieMuskat. This story was not subject to the approval of Major League Baseball or its clubs.