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.
New Hampshire beats Division III Mount Saint Vincent 100-61
Josh Hopkins scored 15 points, freshman Jayden Martinez had 14 points and eight rebounds and New Hampshire beat Division III Mount Saint Vincent 100-61 on Monday.
Ducks on upset alert this week
Will Villanova and Oregon survive tough tests this week?
Duke leapfrogs Kansas for No. 1 in latest AP Top 25 poll
Duke has supplanted Kansas atop the new AP Top 25 poll after its dominating win against Kentucky, giving the Blue Devils a record number of appearances at No. 1.