Hill had 12 of his points on four straight 3-pointers as the Vandals (10-16) of the Western Athletic Conference took control of the game with a 16-5 run.
Idaho only had one basket over the final 5:27 but connected on 12 of 13 free throws.
Kyle Barone added 12 points and Mike McChristian scored 10 for Idaho.
Chris Hansen led Idaho State (5-21) with 19 points. Tomas Sanchez added 18 points and Morgan scored 10.
The win was Idaho’s first in Pocatello since 1996. The Vandals will rejoin the Big Sky Conference in 2014 for basketball and all sports but football, where they will be independent.
The game was part of the BracketBusters series, but the 101st between the schools.