Mike Burwell added 13 points, while Rafriel Guthrie and Jerrelle Benimon each scored 12 for the Tigers (25-10), who were coming off their first-ever postseason victory on Wednesday night versus USC Upstate thanks to a half- court heave by McGlynn at the end of regulation.
Towson, which has won nine of its last 10 games, shot 50.9 percent from the field. advances to the quarterfinals.
Rashawn Rembert scored 17 to lead East Tennessee State (19-16), which dismissed the Chattanooga Mocs in the first round. The Buccaneers also received 14 points from Hunter Harris, and 11 apiece from Kinard Gadsden- Gilliard, Jalen Riley and Lester Wilson.
ETSU scored 12 of the game's first 14 points, but the Tigers later went on a 13-0 run to grab a 24-22 edge on McGlynn's 3-pointer. Towson held a 40-34 lead at the half.
Marcus Damas hit a jumper for a 46-36 cushion with 17:34 remaining, and the Tigers were in front by at least four the remainder of the game. Towson built its lead to as many as 15 midway through the half and made enough free throws down the stretch.