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.
LGBT community has 'bullied the American people': Bachmann
McPhee, Cokas 'working on their marriage' after affair