Gudmundsson tied the game at 50-all on a three-point play with 2:34 to go.
Ball State (1-3) lost its second straight in the tournament will try to avoid going 0-for-Charleston against the Appalachian State-Wichita State loser. He put Davidson up for good on a 3-pointer with 51.2 seconds left.
They'll face Davidson, which rallied from 10 points down in the second half to defeat Wichita State.
Alabama basketball's ice-cold shooting Thursday provided the wakeup call the Crimson Tide needed as it regrouped to blow out Ball State 79-61 Friday.
They seized control in the first half against Northeastern, going from trailing 24-23 to leading 46-26 at the break.
Justin Forrest had 14 points to lead Appalachian State (1-2).
"None of us here have been able to do it, so this means a lot", said Hokies guard Nickeil Alexander-Walker, who scored 20 points.
Virginia Tech will play the victor of the next game, Alabama vs. Northeastern, in Friday's semifinals.
Man's runny nose was actually leaking brain fluid
Phillpotts said he had been battling what he thought were allergies during the past five years. Other doctors had reportedly diagnosed Phillpotts with pneumonia and bronchitis.
Ball State (1-2) was led by Tayler Persons with 21 points. The Cardinals will play the Alabama-Northeastern loser Friday.
The games will be played Thanksgiving week, November 21, 22 and 24 at the TD Arena, home of College of Charleston.
The Gators are 46-24 all-time against the Hurricanes, a two-time champion of the Charleston Classic (2009, 2014), including 5-3 in the last eight meetings with their last in November 2016.
No. 16 Virginia Tech and No. 23 Purdue will get their strongest tests of the early season when they play in the Charleston Classic. Alabama shot 47 percent in the first half while holding Ball State to 28 percent, including 0 of 7 from 3.
Wichita State (1-2) could not recover.
Other games in the first round include Alabama (2-0) of the Southeastern Conference against Northeastern (1-1) and Wichita State (1-1) against Davidson (2-0). Edwards had two 3-pointers in the stretch.