Southern (17-16) will face second-seeded Alabama State (19-9) on Friday in the semifinals.
Alabama A&M led by two at the half, but Southern took the lead early in the second half and led by as many as 10 twice. But the Bulldogs cut it to three with 1:13 left on Ladarius Tabb's 3-pointer.
Lynch responded with a jumper at the other end and after Rakiya Battle missed a 3-pointer for Alabama A&M, Rogers made four consecutive free throws to seal the win.
Alabama A&M (9-20) was led by Battle and Nicholas West with 15 points apiece. Tabb finished with 14. The Bulldogs were 4 of 17 on 3-point attempts.