Liberty (14-10, 5-6 Big South) beat Winthrop 73-70 earlier in the year, which gave the Flames their first regular season sweep of Winthrop since the 2003-04 season.
James was 9 of 15 from the floor with eight rebounds and three blocks. Homesley drilled 4 of 5 from distance and Georgie Pacheco-Ortiz added 14 points with five assists and three steals for Liberty, which has won two consecutive after dropping five straight games.
The Flames never trailed, jumping out to an early lead and holding a 37-26 halftime advantage. They pushed their lead to 58-44 following a Lovell Cabbil 3 at the 10:57 mark.
Xavier Cooks had 21 points and nine rebounds for Winthrop (13-9, 7-4), which had won six straight before facing the Flames.
Mannion, who recently reclassified and is ESPN's No.11 overall player in the class of 2019, chose Arizona over Marquette.
He'll fit in with Sean Miller's plans for a faster tempo on offense.
The cream of the crop of American high school basketball will congregate in Colorado Springs from Oct. 5-7, as USA Basketball unveils its newly expanded Junior National Team minicamp in collaboration with the NBA, NCAA and NBPA.