Fulmer (3-6) was one strike away from setting a season-high with 10 strikeouts while taking a 2-0 lead into the seventh, but Gennett crushed a 1-2 fastball into the seats in right field to tie the game with his 13th home run of the season.
Then Suarez hit the next pitch off what appeared to be the yellow padding in left field. But after a crew chief review it was determined the ball cleared the padding for Suarez's team-leading 15th home run of the season.
The back-to-back blasts – the third of the season for the Reds – made a winner of Cincinnati starter Tyler Mahle, who allowed two runs in six innings with eight strikeouts and four walks.
›› RELATED: Reds notes on Peralta’s struggles, Hamilton’s surge, Votto’s climb
“Tyler did a great job,” Reds manager Jim Riggleman said. “Getting six or eight innings out of your starters gives you a chance to win and use your bullpen the way you want to use them.”
Mahle (6-6) gave up solo home runs to Jeimer Candalario in the first and Niko Goodrum in the fourth before stranding a pair of runners in the fifth and, after a visit from Riggleman, getting out of a bases-loaded jam in the sixth with a strikeout of Fulmer.
“That was huge,” Mahle said of Riggleman’s decision to leave him in the game. “Sometimes we get pulled before we want to, but today when he went out there I expected to get pulled. Two outs and I walk a guy and give up a double. In a situation like that you expect to get pulled, or at least I do."
But after Riggleman ordered an intentional walk of Dixon Machado to load the bases, Mahle punched out Fulmer for season high-tying eighth strikeout.
Scott Schebler, who went 2-for-5, rode the momentum of that punchout and got the game-winning rally started with a leadoff double in the sixth. After Tucker Barnhart flew out and Joey Votto struck out, Gennett tied the game with his homer, just the fourth hit of the day for the Reds.
And Fulmer never recovered. After giving up the go-ahead homer to Suarez, he walked Jesse Winker to end his day. Fulmer went 5.2 innings, giving up three runs on five hits with nine strikeouts and two walks.
Follow Jay Morrison on Twitter
The Reds got an insurance run in the seventh when Barnhart’s second single of the game scored Billy Hamilton.
Votto followed with a walk to load the bases with no outs. But the Reds failed to blow open the game when Gennett and Suarez each hit shallow fly outs and Alex Blandino struck out.
“We were holding out breath a little bit because we had bases loaded and didn't any any more,” Riggleman said.
The Tigers got within 4-3 in the eighth on a pair of two-out infield singles. Jacoby Jones hit a high bouncer between Suarez at third and reliever Jared Hughes. Jones stole second and came across an unattended home plate when Machado beat out a 10-foot chopper that pulled Barnhart out of position.
Adam Duvall, who stayed in the game after pinch-hitting in the sixth, got the run back with a solo home run, his 12th homer of the season, with one out in the bottom of the eighth.
›› MORE: Votto does bird a favor with grand slam
Billy Hamilton followed with a ground-rule double for his second hit of the game, giving him three consecutive multi-hit games. That last time that happened was July 2016.
Raisel Igelsias pitched the ninth and worked around a two-out single to record his 11th save.
The Reds win was their sixth in eight games.
“The way we’re playing right now is how we expected to play all year,” Gennett said. “If our pitching can keep us in the game, it’s only a matter of time before we get a few runs across.”
The homestand continues Thursday night when they open a four-game series against the Chicago Cubs.