Jul. 25—CINCINNATI — The heat index had been rising all weekend, leaving the air, like the standings, thick and muggy, uncomfortable and, in a few places, oppressive.

And that was just in the Cardinals’ dugout.

On a hot, humid, sticky afternoon along the Ohio River with a game-time temperature of 88 degrees, the Cardinals’ offense started cooking, but not before frustrations with the umpiring crew and recent results reached a boiling point.

Manager Mike Shildt, irked he didn’t get time to challenge a call in the field and fed up with the strike zone and previous irritations over the weekend, was ejected in the third inning. So at least he had the option to watch from an air-conditioned office. From there, he would have seen the lineup he’s been preheating all month ignite.

All three Cardinals outfielders homered, two in the decisive seven-run fourth inning, and Nolan Arenado had a triple and his 20th home run of the season. The Cardinals seized a six-run lead early and held on for a 10-6 victory against Cincinnati at Great American Ball Park.

“We’ve been saying every game is a must win,” said center fielder Harrison Bader, whose three-run homer was the punctuation on the fourth-inning splurge. “Go down two in a series, get an off day (Monday), doing everything we can to find a way to win. The way we played proves we can do it.”

The win snapped a sixgame losing streak to Cincinnati.

Shildt snapped six innings earlier.

Dylan Carlson came close to legging out an infield single to lead off the third inning, and the play was close enough for the Cardinals to consider a challenge. Shildt asked for a pause in the game, but as they decided on requesting a replay, home plate umpire Chad Fairchild waved them off, saying they’d run out of time. Shildt trotted onto the field to confront Fairchild and crew-chief Ron Kulpa, delaying the game more than a replay would have taken.

“That was a little bit the proverbial straw that broke the camel’s back from this series,” Shildt said. “This has been a series that didn’t taste really great from our perspective. This series took a lot of exceptions.”

Shildt had receipts.

On Friday night, both sides were agitated by home plate umpire C.B. Bucknor’s strike zone. A detailed accounting of the calls that made its way through the Cardinals’ clubhouse had a freckling of pitches inside the zone called balls, including a pivotal one as the game came undone against the Cardinals’ bullpen. There were four calls that went against the Cardinals that were overturned by replay. An infielder was tagged with a visit to the mound with which Shildt disagreed.

Later Sunday, Genesis Cabrera delivered a 3-2 pitch in the zone that was called a ball for a leadoff walk. Cabrera was leaving the game as he stuck out his tongue and said something to Fairchild, prompting his ejection. And then there was the replay. Facing a second consecutive sweep to Cincy, tensions were high and Shildt was denied the chance to challenge.

Kulpa told a pool reporter that Fairchild first asked for Shildt’s decision.

“We still didn’t get an answer,” Kulpa said. “The clock expired. It got past zero and we denied the challenge. We said you didn’t give us an answer in time.”

Managers have 20 seconds to make the call, per MLB’s replay guidelines.

Between halves of the third inning, Shildt returned to the field and notified Kulpa and Fairchild that he checked the clock, and it was 27 seconds. He noted times he had seen teams receive some flexibility, and he also had some thoughts on the other calls.

“I’m trying to tell you there’s an accountability to it at some point,” Shildt said. “I took exception. I said my piece. Said my piece about some other things. At some point, you’ve got to stick up for your guys. We can be patient, but we’ve got competition here that is sincere. The whole series it was like, ‘You’ve got to be kidding me.’”

For the fourth time this season and the second time in a week, Shildt was ejected, and this time he served as a valve, releasing all sorts of overheated frustration from his clubhouse.

‘Always fighting for us’

That’s when the offense caught fire.

“It’s the big leagues. There’s tension around every corner,” Bader said. “It’s just a matter of how you respond to it. He got me pumped up, fighting for us. He’s always fighting for us. I respect the hell out of that.”

Tyler O’Neill claimed a lead for the Cardinals with a two-run homer in the first inning. Joey Votto answered with a three-run homer in the bottom of the inning.

There the score chilled, 3-2, as temps rose, sweat soaked, and O’Neill’s spot in the order came around again to lead off the fourth inning. In the past month, the Cardinals have retooled their offensive approach — talking openly about using more of the field, about reconnecting with their onbase roots. Shildt on Sunday morning said he wants the lineup to be “multi-dimensional.”

In the fourth inning, the Cardinals put that approach in the microwave.

O’Neill drew a walk. Paul DeJong followed with an infield single — on a play in which, yep, Bucknor called an out but didn’t see the ball bounce. Replay did. Reds starter Sonny Gray allowed extra-base hits to the next three batters. An RBI double from Tommy Edman came ahead of Bader’s three-run homer, and Andrew Knizner followed with a double. Two batters later, Carlson lofted a tworun homer down the right field line for his 10th. Carlson’s homer chased Gray, and Arenado greeted his replacement with a triple and then scored on a wild pitch for the inning’s seventh run.

With that gust at his back, rookie Johan Oviedo had the runs and clear runway for the first big-league win of his career. He came two outs shy. The righthander exhausted his pitch count and the Cardinals’ latitude with two walks in the fifth inning that loaded the bases. He needed 98 pitches to get 13 outs, and contributing to the bloat was six walks.

He was blunt about chasing that first win now into his 19th start.

“Bottom line: I have to stop throwing walks,” Oviedo said. “I’m tired of it. I’ve got to stop.”

Reliever Ryan Helsley received the win for retiring two batters in Oviedo’s place and stranding all three Reds to end the fifth inning. Gio Gallegos slipped free of a similar bind in the eighth before Arenado’s homer made Alex Reyes ineligible for a save in the ninth. Given the heat of the day and the temperature of the series, the extra run was as close to a breeze as there was.

One hundred games into their season, the Cardinals are perched at a poetic 50-50.

Coin flip.

Could go either way from here.