East Tennessee State (16-10) scored the first seven points of the game, including Riley's 3-pointer, and led 47-41 at intermission.
A 10-2 run early in the second, punctuated by Dwan Caldwell's jumper, lifted Tennessee Tech to its first lead of the night, 56-55, with 12:43 to go.
ETSU's Lester Wilson broke a 70-all tie with a 3-pointer with 5:21 left, and then Riley added a jumper and a pair of free throws before drilling a 3-pointer to put the Buccaneers up 80-74 with 2:14 remaining.
Rembert finished with 17 points and Wilson ended with 15.
Torrance Rowe paced Tennessee Tech (12-15) with 22 points.