American Ginepri, who won the Indianapolis title in 2005 and reached the semi-finals last year, was upset by 83rd-ranked Michael Berrer of Germany 3-6 6-2 6-1.
Kubica won the race in his fifth attempt, his first three in the second tier LMP2 category, to become Poland's first overall winner since Le Mans was first staged in 1923.
Top seed James Blake overcame a patchy service game to defeat South Korean qualifier Woong-Sun Jun 6-3, 7-5 and reach the quarter-finals of the Indianapolis Tennis Championships on Thursday. Blake, ranked eighth in the world, made just 49 percent of his first serves but converted three of nine break points to defeat the 293rd-ranked Jun in 71 minutes.
Summary of sports events and persons who made news on Monday
Donald Trump virtually sealed his Republican nomination for the United States presidential polls on Tuesday night after he scored a major win at the Indiana primary and his nearest rival Texas Senator Ted Cruz bowed out of the race.
Summary of sports events and persons who made news on Thursday
Summary of sports events and persons who made news on Thursday
A summary of sports events and persons who made news on Monday