Hill, who had his seventh double-double of the season by adding 14 rebounds, had three free throws and Horne had a breakaway away dunk in the final 53 seconds to help Arizona (6-2) score the final 11 points of the game.
San Diego State (7-2) didn't score the final 4:16 after D.J. Gay hit a pair of free throws to trim the Wildcats lead to 58-56.
Horne was scoreless before making four free throws and a follow-up dunk to put Arizona ahead 62-56 with 3:01 remaining.
Tim Shelton led the Aztecs with 13 points.