Z. Mason and Drazen Zlovaric added 10 apiece for Chattanooga, which shot 54 percent (13 of 24) in the opening frame en route to a 38-37 halftime lead.
Elon (19-9, 12-4 Southern Conference) opened the second half on a 16-9 run go up 51-46 but Chattanooga clawed back to a 59-56 advantage midway through the frame.
Ryley Beaumont cut it to 59-58 with a layup but the Phoenix would get no closer, as Chattanooga (12-17, 7-9) used a 10-4 run to pull away. McGhee scored seven points during the spurt.
Elon shot 42 percent (23 of 54) but went 1-of-5 shooting over the final 3:33. Chattanooga shot 51 percent (24 of 47) and made 20 free throws. The Phoenix shot just 14 free throws.
Beaumont paced Elon with 20 points.