The Tigers (4-8) outscored the Hornets 12-6 in the extra period after overcoming a seven-point deficit in the second half.
Alabama State (3-11) blew the lead in regulation thanks to poor free-throw shooting, finishing at just 38.2 percent (13 of 34). Jackson State made 21 of 32 free-throw attempts (65.6 percent), including all six in overtime.
Offense was at a premium throughout the game as the scoreboard remained untouched until Kenderek Washington's free throw for Alabama State 2:10 into the contest.
Grant Maxey chipped in 11 points and nine rebounds for the Tigers, who trailed 22-18 at halftime.
Tramaine Butler had 12 points and Washington added 10 for the Hornets, who lost their fifth straight.