Riddle was 21 of 30 for 160 yards and Newsome rushed for 161 yards on 25 carries for the Phoenix (5-1, 3-0 Southern Conference), who never trailed.
Jordan Sorrells was 26-of-43 for 248 yards and one touchdown for Furman (4-2, 1-1).
Riddle hit Newsome on a 1-yard score and a 24-3 lead with 2:19 left in the third quarter.
Sorrells threw a 3-yard touchdown pass to Chris Truss to cut the lead to 24-10 with 8:16 left in the game before Newsome scored on a 9-yard run to cap the scoring with 2:17 remaining in the game.
Newsome also caught six passes for 29 yards.