Kimball seized the lead from Pagenaud with 18 laps remaining and held on for his first triumph in 45 IndyCar starts, giving Chip Ganassi Racing its fourth consecutive victory this season.
It was also Gnassi's fifth straight win at the 2 1/4-mile Mid-Ohio road course.
Kimball joined James Hinchcliffe, Takuma Sato and Pagenaud as a first-time winner this season.
Scott Dixon, seeking a fourth triumph in four IndyCar races, ended in seventh place.
Benedict Cumberbatch's dramatic reading of R. Kelly lyrics is just what you need
Kate Middleton recycles dress at movie premiere