Arizona was trailing 3-1 in the bottom of the fifth when pinch-hitter Jason Kubel drew a one-out walk from Braves starter Tim Hudson, went to second on Gerardo Parra's infield single and then scored when Didi Gregorius singled to center.
After Paul Goldschmidt struck out, Chavez cranked a 1-1 pitch into the left-center gap that rolled to the wall, sending home Parra and Gregorius and putting the Diamondbacks up 4-3.
Chavez scored an insurance run when Cody Ross added a single and Arizona went on to claim the rubber match of a three-game series.
Ian Kennedy (2-3) earned the decision, yielding three runs on five hits over five innings.
Hudson (4-3) yielded five runs on eight hits over five frames.
Freddie Freeman went 3-for-4 with three RBI for Atlanta.