CINCINNATI -- Josh Hader made history in the Brewers’ 5-4 win over the Reds on Tuesday, though the story of how he came to be on the mound at Great American Ball Park with the slimmest of leads was just as compelling as the finish.

Hader issued a leadoff walk, but then retired three batters in a row, the last two on swinging strikeouts, to give him 500 strikeouts in 293 2/3 career innings. He’s the second-fastest in history to reach that milestone, just behind Aroldis Chapman (who reached 500 strikeouts in his first 292 innings) and ahead of Craig Kimbrel (305 innings).

“It’s a great feeling to be a part of that group, elite closers like that,” said Hader, whose 44.4 percent strikeout rate is highest ever for a pitcher with at least 20 career innings. “You can even add Kenley [Jansen] in there, too. Those guys, they’re different. To be a part of that is special.

“It’s not easy. All of them worked hard to get where they’re at, and that’s the drive you feed off of.”

Here’s more history: Hader is the third pitcher since the save became a stat to log one in each of his first 12 appearances in a season. Lee Smith did it for Baltimore in 1994, and Jose Mesa for Pittsburgh in 2005. If the circumstances align, Hader could be the first to record a save in each of his first 13 games.

"If it's possible, it feels like he's getting even better and that's what makes it so impressive,” Brewers manager Craig Counsell said. “What he seemingly continues to do is improve on greatness."

Now, here’s the story of how the Brewers got to Hader in the first place.

“I say this to myself every time,” Hader said. “It’s a rollercoaster ride.”

The real drama started after Freddy Peralta set a season high with eight strikeouts in what he called “a big step for me,” and after the Brewers weathered a much more formidable Reds rookie Hunter Greene less than a week after facing him for the first time, and after the bottom of Milwaukee’s batting order did the heavy lifting to turn a 1-1 tie after five innings to a 5-1 lead going into the bottom of the eighth.

Along the way, Christian Yelich made the play of the night, or so the Brewers’ thought at the time, when he laid out for a five-star catch to end the bottom of the seventh. That’s the highest rating for a defensive play by Statcast, which estimated a 25 percent catch probability.

Brent Suter and Brad Boxberger had already pitched, Trevor Gott was down because of a minor quad issue and Devin Williams hadn’t worked in five days, so Williams was Counsell’s choice for the bottom of the eighth with a four-run lead. Things began smoothly enough with a pop out to start the inning, but then got tough: The Reds loaded the bases with two walks and a single before Williams struck out Tyler Stephenson for the second out. With two outs and two left-handed hitters due up, Hader did not warm in the bullpen; the Brewers have rarely used him for multi-inning saves in recent seasons. They instead began to ready Luis Perdomo, who just arrived from Triple-A Nashville last week and has only made one Major League appearance this season.

Williams, pushing over 30 pitches, walked Colin Moran on four straight balls to force in a run, then methodically battled Tyler Naquin for six pitches. The sixth -- Williams’ 38th pitch -- was Williams’ signature changeup. Naquin pulled it into the right-field corner for a two-run double that made it 5-4.

That’s when the Brewers went to Perdomo. He jammed Kyle Farmer, who sent a spinning flare up the middle. Luis Urías, who’d homered off Greene in the fourth inning and was starting at shortstop on the first day this season that Willy Adames didn’t start there, made a diving catch to save the Brewers from falling behind by a run.

“Everything went fast and when I caught it -- to be honest, I didn’t think I would catch it,” Urías said.

“I was just hoping he'd keep it in the infield, and he ended up making a great catch,” Counsell said.

Said Reds manager David Bell: “I’m still trying to process the defense. It’s fun to watch except when it beats your team.”

With that, the Brewers passed a lead to Hader.

Nothing is 100 percent in baseball, Urías noted, but with Hader, he said, it’s close.

“It certainly makes my job a heck of a lot easier,” Counsell said. “He's just been so good. He's just locked in and he just gets the job done. It's not something we ever take for granted, but the way he does it is just so, so impressive.”