Elon (15-17) will play top-seeded William & Mary in the quarterfinals on Saturday.
In overtime, Tanner Sampson and Austin Hamilton nailed back-to-back 3-pointers to put Elon up by six. Four McGlynn's three-point play cut it to three, but Towson fumbled on the next possession, and Kevin Blake took it the other way for a dunk to seal it.
After six lead changes in the second half, Towson's Mike Morsell came up with a steal with 30 seconds left and the Tigers down by two. After a Towson timeout, Austin Hamilton fouled McGlynn, who hit both to tie it at 62 with 19 seconds left. Hamilton missed a jumper with 3 seconds to send it to overtime.
Hamilton and Sampson both ended with 12 points for Elon.
Morsell led Towson (12-20) with 18 points and McGlynn finished with 13.