The D-backs tied the game when Ender Inciarte followed the singles by grounding into a fielder's choice off Ross Detwiler allowing Ahmed to score from third.
The Braves grabbed a 1-0 lead in the fifth when Jace Peterson scored from third on Michael Bourn's grounder to short that was booted by Ahmed.
It is the second no-hit bid Miller has lost this season. On May 17 in Miami, Miller was one out short of a no-hitter until Justin Bour singled to break it up. Miller finished that game with a two-hitter, and it was the last victory for the Braves' right-hander.