Horton, ranked fourth nationally at 13 rebounds per outing and third in double-doubles (7), also grabbed 13 rebounds and the Governors (4-5) outrebounded the Trojans 42-31, scoring 17 second-chance points off 14 offensive boards.
Kahlil Davis scored 16 with four 3-pointers and Austin Peay made 21 of 27 free throws (78 percent).
Trailing 36-31 at halftime, Troy led 41-38 after Jordon Varnado's 3, but the Governors were up 62-51 after Terrell Thompson hit a layup with 8:05 left and held on despite three Troy 3-pointers in the final 2:38.
Jeremy Hollimon scored 25 points with six 3-pointers, both season highs. Varnado finished with 13 points, and Wesley Person Jr. had 12 with four 3-pointers for Troy (4-4). Person has scored a 3-pointer in 37 consecutive games, the longest active streak in the nation.