The Bulldogs (4-11-0, 3-4-0) built a 3-0 lead early in the second half only to see the Runnin' Bulldog use an own goal and two more goals to tie the match at 3-3 and send the game to overtime.
In overtime, Katie Soles scored on a breakaway with four seconds left in the first overtime period to give the Runnin' Bulldogs the dramatic victory.
Asheville opened the scoring in the fourth minute when junior Ferriss Roberts scored her third goal of the season off an assist from Leilani Halkiotis.
Freshman defender Margo Flewelling tallied her first career goal in the 14th minute. She took a pass from Roberts and hit a shot from 10 yards out to push the lead to 2-0.
The Bulldogs led 2-0 at intermission.
In the second half, senior defender Frances Staelin scored her first career goal. Off a corner kick, Halkiotis sent a ball in the box that Staelin booted it in from 12 yards out give Asheville a 3-0 lead at 52:56.
The GWU comeback started four minutes later when Dawn Rollyson scored in the 56th minute to cut the lead to 3-1.
Thirty seconds later, the Runnin' Bulldogs caught a huge break when they scored an own goal on an Asheville clearing that went into the back of the net to narrow the lead to 3-2.
Megan Reynolds tied the match in the 65th minute on an unassisted goal to make it 3-3.
The Bulldogs are back in action Saturday night at Winthrop starting at 7 p.m.