Steven Zoidack scored for Berea (9-4-2) with 3:48 left in the first half to tie the game at 1-all, and Noah McGraw scored the winning goal with 10:25 remaining.
"We're having problems of letting down toward the end of each half," Danville coach Gary Reynolds said.
Danville (8-8-1) led after Chris Bright's goal off a Jeff Ricker corner kick 9:45 into the game, but Reynolds said the Admirals weren't sharp in the first half.
"We were not aggressive in the air at all in that first half, and we lacked a lot of communication, even though we were hanging in there pretty well with a very good team," he said.
It was the third straight loss for Danville, which outshot Berea 0-8.
"We've got a lot of things to work on, and we're kind of down right now," Reynolds said.