The Jaguars (13-9, 10-4 Sun Belt Conference), who have won five of their last six games, started 4 of 13 from the free-throw line, then closed the game with 20 straight.
South Alabama trailed 43-35 with 12:40 left before launching a 20-5 run to lead by seven with 5:15 remaining.
The Trojans (10-14, 5-8) got to 61-60 with 19 seconds left on Hunter Williams’ 3-pointer, but Dre Conner answered with two foul shots and Javier Carter blocked a Troy 3-pointer.
After Emil Jones, who led the Trojans with 23 points, hit two free throws, Rubit, who was 11 of 15 from the line, made his final two foul shots with 2 seconds remaining to seal it
The Jaguars are now 1-9 when trailing at halftime.