Astros pinch-hitter Aledmys Díaz blooped a leadoff single in the eighth to break up the no-hit bid. Left fielder Eddie Rosario appeared to hesitate and the ball fell just in front of his glove.
Austin Riley hit an RBI double in the third off Astros starter Luis Garcia and Travis d'Arnaud homered off Kendall Graveman in the eighth.
Anderson was pulled after five innings and 76 pitches with a no-hitter intact. Relievers A.J. Minter and Luke Jackson kept Houston hitless until Díaz singled off Tyler Matzek.
Braves closer Will Smith worked around a leadoff single in the ninth by Alex Bregman.
Game 4 is Saturday night at Truist Park in Atlanta.