Streit, who earlier in the day needed 24 holes to defeat Marianne Towersey, never led in the final match until winning the last hole of the duel on the Foothills course at Barton Creek Resort.
Streit fell behind with a bogey at the first and another bogey on the third dropped her two back of Fitzgerald, who knocked off four-time defending champion Carole Semple Thompson in the semifinals. The loss for Thompson was her first in the senior match play event, as she had won 28 straight matches.
Fitzgerald's lead slipped to a 1-up advantage when Streit birdied the par-5 fifth. Fitzgerald however won the next hole to go back up by two.
Streit, who previously won this title in 1985 and 1994, won the ninth to get back within 1-down, but Fitzgerald again answered with a win at the next. This time though Streit responded with wins at the 11th and 13th to square the match.
Fitzgerald, the 1997 Senior Women's Amateur champion, reclaimed the lead with a par at the 14th. After three straight halves, Streit evened the match on the 18th hole thanks to a bogey by Fitzgerald.
The duo battled through four extra holes, halving each of them. Streit claimed the championship on the 24th hole when she saved par and Fitzgerald stumbled to a bogey.