Hoosier starter Kyle Hart (2-1) allowed only two runs on five hits over eight innings, striking out eight and walking none. Indiana (8-6) put an end to 18-game hitting streaks by UK's Kyle Barrett and A.J. Reed.
No. 20 Kentucky (13-4) dropped its first game to IU in the last four meetings. It was the first matchup between the two programs as Top 25 opponents.
Dustin DeMuth and Kyle Schwarber each homered for Indiana.
The Cats got two hits from Max Kuhn, including his second home run of the season. Micheal Thomas also had two hits for UK, while Austin Cousino added an RBI double.
UK returns to action on Wednesday, playing host to Northern Kentucky at 4 p.m. ET at Cliff Hagan Stadium.