The Jaguars (2-6) trailed the NAIA Bleu Devils (2-11) 39-36 at the half but used a 15-0 surge in the middle of the second half to take control.
Jared Sam started the game-changing run with a three-point play. Adrian Rodgers followed with a 3-pointer to put Southern up 47-45 with 12:40 left. Sam added another basket before Lynch knocked down a 3-pointer and then Joell Hopkins had a pair of baskets to make it 56-45 with 7:17 remaining.
Hopkins finished with 12 points and Sam 10.
Dillard was led by Houston Chatman with 20 points. Lynch hit five 3-pointers and led the Jags with five rebounds and five assists.
The Bleu Devils got off to a quick start, grabbing a 13-4 lead and then closed the half with an 8-2 run.