Trailing 14-10 at halftime, Jeanty hit Clayton Granch with a 1-yard scoring pass on the Aggies' opening drive of the second half.
On the next possession, Leahy put together a 15-play, 78-yard drive capped by Rose's 2-yard plunge and the Aggies (1-8, 1-4) led 24-21. After forcing Texas state to punt, Leahy hit Rose in the flat on the next possession and Rose raced 77 yards for the score.
Jeanty was 24 of 45 for 297 yards passing.
Jones ran for two TDs and was 21 of 36 for 287 yards passing with two interceptions, each grabbed by Jacob Nwangwa.