South Alabama (12-9, 9-4 Sun Belt) used a 19-7 run mid-way through the first half capped off by Allen's lay-up to gain an early lead and make it 26-14 with 6:01 remaining in the first half.
Arkansas-Little Rock (14-10, 8-5) made things interesting late in the second half by completing a 16-8 run over a 7-minute stretch when Ben Dillard sunk a lay-up to cut South Alabama's lead to three, 64-61, with 1:48 to play.
Dillard ended the night with 15 points.
Ammons and Allen hit consecutive lay-ups in the last 47 seconds to extend the Jaguars' lead to seven, 68-61, which was all the cushion South Alabama needed.
The Jaguars shot 41.2 percent from the field and were 23 of 33 from the free-throw line.
Mike Krzyzewski says he has good reason to be excited for next season thanks to a combination of Duke's incoming freshmen and a core of experienced upperclassmen.
Georgia guard Juwan Parker has been awarded a medical redshirt, leaving him with two years of eligibility, after missing the 2015-16 season with a partially torn Achilles tendon.
Forward Trevon Bluiett has withdrawn from consideration from the NBA draft and will return to Xavier for his junior season.