Sheehey collected a loose ball off a blocked shot and fired it home for the Hoosiers (27-8), who advanced to the Sweet 16 in their quest for their first NCAA title since 1987.
Christian Watford added 16 points and Cody Zeller also put in 16 to go with 13 rebounds for fourth-seeded Indiana.
The 12th-seeded Rams (29-7) got 15 points and seven boards from Bradford Burgess but it wasn't enough down the stretch for VCU.
Rob Brandenberg added 13 points for the losers.
Notable deaths of 2014 [PHOTOS]