With two outs in the 11th inning, Spencer Steer reached on an infield single against Nabil Crismatt (0-2).
Designated runner TJ Friedl moved to third base on the play and scored when Crismatt committed a balk.
Lucas Simas retired the three batters he faced, including the last two on strikeouts, in the bottom of the 11th to earn his third save.
The Reds, who trailed 4-0 after five innings, rallied for three runs in the 10th inning behind RBI doubles hit by Spencer Steer and Nick Martini and a run-scoring single hit by Christian Encarnacion-Strand.
All the hits came against Arizona reliever Miguel Castro with no outs.
Arizona opened the 10th with Geraldo Perdomo bringing home the designated runner at second base with a double against Cincinnati stopper Alexis Diaz, who entered with 34 saves.
Corbin Carroll followed with a walk.
With one out, Tommy Pham was safe on a fielding error by second baseman Matt McClain, allowing Perdomo to score to cut the lead to 8-7.
Carroll moved to third on the play.
Christian Walker followed with a sacrifice fly to deep center field to bring home Carroll.
Diaz (6-4) was the winning pitcher.
Cincinnati scored twice in the ninth to tie the game at 4 and give Diamondbacks closer Paul Sewald his fifth blown save.
Noelvi Marte led off the ninth with a walk off Sewald, who has 28 saves.
With one out, Tyler Stephenson hit a double to bring home Marte, who had stolen second and advanced to third on a flyout.
Friedli reached on a bloop single to right field and moved to second on an attempt to retire pinch runner Michael Siani at third.
McClain followed with a groundout that enabled Siani to score to tie the game.
Arizona starter Zach Davies (lower back inflammation) was activated before the game. He allowed one run in five innings while striking out five and walking two in his first appearance since July 18.
Cincinnati's Ben Lively (pectoral) was also activated from the injury list Saturday.
He pitched 5 2/3 innings in relief and allowed three runs on six hits with five strikeouts and no walks.
—Field Level Media