Jay Bruce's second home run of the game gave the Reds a 3-2 lead in the top of the ninth.
Paul Goldschmidt singled past
Joey Votto at first base leading off the bottom half before Chapman (3-3) issued consecutive walks to Miguel Montero and Cody Ross. With the infield drawn in, Kubel singled over second base for his third career game-ending hit and first since May 22, 2010.
Brad Ziegler (4-1) replaced Heath Bell after Bruce's second home run and earned the win.
Gerardo Parra hit a two-run homer for Arizona.
Starting pitchers Mike Leake and
Patrick Corbin dueled for eight innings before turning the game over to the bullpens.
Leake retired the first 15 batters he faced and scattered four hits over eight innings with a walk and a strikeout for the Reds, who have lost three straight.
Corbin allowed two runs on four hits over eight innings and was handed his fourth straight no-decision in his quest to become the first Diamondbacks pitcher to win his first 10 decisions.
Bell, who had converted nine straight saves, came on in the ninth to protect a 2-1 lead. But he walked
Brandon Phillips leading off the inning and Bruce followed with his team-leading 18th homer.
Bruce gave the Reds a 1-0 lead when he led off the second inning with a line drive to the balcony overhanging center field, about 20 feet from where his ninth-inning shot landed.
The 472-foot drive was the longest home run at Chase Field this season and the fourth-longest ever by an opponent. Bruce has homered in seven of his last nine games.
Corbin broke up Leake's nascent bid for a perfect game when he looped an opposite-field double into the left-field corner with two outs in the sixth.
Two pitches later, Parra drove a cut fastball just over the fence into the pool area in right-center for his second home run in two games to give Arizona a 2-1 lead.
Corbin allowed Bruce's first home run, a single by
Devin Mesoraco in the seventh and Derrick Robinson's one-out triple to center in the eighth.
With Robinson representing the potential tying run, the 23-year-old lefty struck out Shin-Soo Choo and Votto to escape the jam and turn the game over to the bullpen.
NOTES: Chapman's blown save was his first since May 19 at Philadelphia. ... Bruce had his 13th career multihomer game and first this season. ... Two of Corbin's four hits this season have been doubles. ... Corbin's three walks were his most since issuing five free passes against Atlanta on May 14. ... Leake threw only 52 pitches over the first five innings and 92 total. ... Parra's home run was the second allowed by Leake in his past five starts. ... RHP
Randall Delgado will make his second start for the Diamondbacks against RHP Mat Latos in Sunday's series finale. Latos is coming off his first loss of the season Tuesday against Pittsburgh.