CINCINNATI -- Rookie Davis has been working to refine his mechanics, in particular the slider. But a mental adjustment he made after allowing seven earned runs in two innings at Milwaukee last week was the biggest difference.

"Just simplifying the game as much as possible," Davis said. "Take the extras out of it. Whenever I'm out there, it's my mound and I have to treat it that way."

Billy Hamilton and Eugenio Suarez each hit three-run homers, and Devin Mesoraco added a solo shot, helping Davis post his first major-league win in the Cincinnati Reds' 7-2 victory over the Pittsburgh Pirates on Wednesday night at Great American Ball Park.

Davis (1-1) pitched five shutout innings with three walks and two strikeouts in his fourth career start and second since spending two weeks on the disabled list with a bruised right forearm.

Simplification came in handy for Davis when he faced jams in four of his five innings. In the third, Josh Harrison was on third doing his best to distract the rookie right-hander, to no avail.

"All his movements out there ... if you're going to steal home, go ahead," Davis said. "It's situations like that. Any extras going on doesn't matter. Just compete and throw strikes."

Suarez hit his sixth homer of the season, but the homers by Hamilton and Mesoraco were their first in a combined 526 at-bats.

Hamilton homered for the first time this season and Mesoraco's solo blast off Trevor Williams in the sixth was his first since Sept. 23, 2104. He had appeared in just 39 games the past two seasons due to shoulder and hip surgeries.

The win assured Cincinnati (13-14) of no worse than a split in the four-game series.

"We want to win the series against them," Suarez said.

Andrew McCutchen hit a two-run homer for Pittsburgh (12-15), his 28th career home run against the Reds and 18th at Great American Ball Park.

Pirates starter Jameson Taillon (2-1) suffered his first defeat of the season, allowing six earned runs in five innings.

"I'm still processing it," Taillon said. "I had trouble with two strikes. I was putting guys on after putting myself in a good position. If there's no runners on, then home runs don't beat you, but two three-run homers do."

Taillon had an 0.47 ERA in three road starts this season before Wednesday. But he wasn't greeted as kindly in Cincinnati.

For the second time in as many as nights, the Reds hit a three-run homer in the first inning to go ahead 3-0. Only this time they held the lead.

On Tuesday, it was Joey Votto. On Wednesday, it was Suarez who crushed a 1-1 pitch to left field with two outs.

Davis threw only nine pitches in the first inning.

He needed 27 to get through the second but pitched out of a one-out, bases-loaded jam. It took Davis 31 pitches to wriggle out of a second-and-third situation in the third.

"I think what was beneficial for Rookie was getting knocked around in Milwaukee," Reds manager Bryan Price said. "He had to get back to simplifying what he does. Pitch to his strengths and stay aggressive. He really had to work for it."

The Pirates went 0-for-7 with runners in scoring position and left 10 runners on base.

"The difference in the game was that number at the end of the box score _ 10," Pirates manager Clint Hurdle said.

With two runners on in the fourth, Hamilton sent Taillon's first pitch sailing into the home bullpen in right field to make the score 6-0.

"That's just kind of his game, just to be a rock in your shoe," Taillon said.

It was Hamilton's first home run in 319 at-bats, at the time the third-longest homer drought in the major leagues.

"I don't do home runs," Hamilton said. "I was looking to get a base hit there. He wanted to go in and left it over the plate. Put a good swing on it."

NOTES: Reds CF Billy Hamilton homered for the first time since June 28, 2016, off the Cubs' Jon Lester. ... Pirates C Francisco Cervelli missed his fourth straight start with right foot soreness. ... Reds RHP Homer Bailey, who remains on the disabled list after multiple arm surgeries, turned 31 Wednesday. He threw a bullpen Tuesday in Arizona and isn't expected back before June. ... Pirates RHP Ivan Nova was named National League pitcher of the month after posting a 1.50 ERA with two complete games during five starts in April.