Stephen Madison added 15 points and Mike McChristian had 10 for the Vandals (6-6, 2-0 Western Athletic), who shot 50 percent from the floor.
James Kinney led San Jose State (7-6, 2-1) with 17 points. The Spartans committed just five turnovers but shot 28 percent from the floor, including 3 for 20 on 3-point attempts.
After Idaho took a 33-30 lead into halftime, Robert Harris opened the second half with a 3-pointer that started a 13-2 Vandals run to make it 46-32. San Jose State got within 53-48 with 8:12 remaining but Idaho scored the next seven points on a pair of Barone free throws, a 3-pointer by McChristian and a layup from Denzel Douglas.