The three were at 15-under-par 198 for 54 holes.
The 47-year-old Perry and Axley shot 4-under 67s and Adamonis had a 66.
Will McKenzie, the tournament's halfway leader, carded a 70 to tie for fourth place one stroke behind with Jay Williamson, who fired a 9-under 62.
Perry has won the Memorial and Buick Open this year. Axley won the 2006 Texas Open. Adamonis is trying for his first tour victory.