The 42-year-old Postillion, a former professional player from Burr Ridge, Ill., who regained her amateur status in 1996, didn't lead until she holed the winning putt.
'I'm relieved,' Postillion said. 'It was a great match. Whichever way it went, it was a great match.'
Cleckler, a 42-year-old Austin city golf course manager who won the Austin City Women's Amateur 14 straight years, earned the final spot in the 64-player match-play field in a playoff Monday morning.
'I was so nervous,' Cleckler said. 'I've played in state amateurs and six or seven Mid-Ams, but I'm so nervous. I squeezed by this morning. I was very shaky. I didn't hit the ball that well. I parred the first playoff hole by making a 15-foot putt, and then made a 7-foot putt for a bogey. That got me in.
'But if I played well in the match, I knew I had a shot.'
Postillion won the 18th hole with a par after Cleckler, 1-up for most of the match, hooked her drive in the water.
'I'm not that disappointed,' Cleckler said. 'This was awesome, awesome. This was huge!'
Defending champion Corey Weworski, 43, of Carlsbad, Calif., advanced with a 4-and-3 victory over Louella Kanew of Los Angeles on the 6,124-yard, par-72 course.
In other matches in the tournament for players 25 and older, three-time champion Carol Semple Thompson, 57, of Sewickley, Pa., defeated Geraldine Doran of Lewisville 6 and 5; 1998 winner Virginia Derby Grimes of York, Ala., beat Charl McLear of McHenry, Ill., 5 and 4; 2002 champion Kathy Hartwiger of Birmingham, Ala., defeated Marti Ross of Dallas 5 and 4; and Robin Burke of Houston beat Martha Leach of Hebron, Ky., 5 and 4.
Three-time champion Ellen Port, 43, of St. Louis was eliminated, falling 1-up to Maggie Leef of Brookfield, Wis.