CINCINNATI -- The New York Yankees went to bed Monday morning in Cincinnati around the time the sun was coming up. But in keeping with the old baseball adage that good hitters can roll out of bed and start swinging the bat, the Yankees did just that.

Brett Gardner and Matt Holliday homered, and Masahiro Tanaka pitched seven solid innings, lifting the Yankees to their sixth straight victory, a 10-4 win over the Cincinnati Reds in the opener of a two-game interleague series on Monday night at Great American Ball Park.

The Yankees (21-9) arrived in Cincinnati at around 5 a.m. ET on Monday after an 18-inning victory over the Chicago Cubs on Sunday night at Wrigley Field.

"Guys are really fatigued," Yankees manager Joe Girardi said. "To end up putting 10 runs on the board says a lot about these guys."

It wasn't a perfect performance for the bleary-eyed Bronx Bombers, who committed two errors. But Tanaka (5-1) gave New York what it needed with the bullpen limited coming off Sunday's marathon. He allowed 10 hits, including a two-run homer by Joey Votto in the seventh. It was Votto's 10th home run this season.

Tanaka gave up four runs (three earned), walked one and struck out six with his 112 pitches, providing a critical respite for a bullpen without closer Aroldis Chapman, Chasen Shreve, Adam Warren, and Jonathan Holder due to their work in Sunday's game.

"He knew it was big for us for him to go a long way," Girardi said. "We created some extra outs for him, but he battled."

Gary Sanchez went 3-for-3 with two RBIs for New York.

Reds starter Rookie Davis, one of the Yankees' top pitching prospects before being traded to Cincinnati in exchange for Aroldis Chapman, allowed five runs (four earned) and seven hits in 4 1/3 innings.

Davis (1-2) retired six straight and struck out the side in the fourth, but the damage was done early, and mostly on his slider.

"It's a work in progress," Davis said of his slider. "I've only been throwing it for two months. It's a matter of finding the right release point. Location-wise, it has to be better."

It was a rough night for Reds pitchers, in particular Drew Storen, who hit three batters in the seventh, including one with the bases loaded to force in a run.

Storen was the first Reds pitcher to hit three batters in an inning since Raul Sanchez on May 15, 1960, versus the Philadelphia Phillies.

"That doesn't happen very often," said Reds manager Bryan Price. "Obviously, there was no intent. That was a very unusual inning, for sure."

Yankees third baseman Chase Headley was hit on the tibia and will be evaluated Wednesday.

"We know he's not trying to do it," Girardi said of Storen. "But it is frustrating. We're already banged up. We're mostly concerned about Chase. It's not what you want to see happen to your guys."

It was bombs-away for the Yankees in the eighth when Gardner and Holliday each hit his sixth home run of the season, off Barrett Astin.

Monday's loss snapped a five-game winning streak for Cincinnati (17-15), which was coming off a three-game sweep of the San Francisco Giants by a combined score of 31-5.

Davis' first career start against his former organization got off to a rough beginning and never got much better.

His fielding error, a walk and a single loaded the bases for Sanchez, who delivered a two-run single. Didi Gregorius followed with a hit to give the Yankees a 3-0 lead in the first.

The Reds, who hadn't allowed a first-inning run in a span of seven days, were behind by three before coming to bat Monday.

Cincinnati got a run back on Votto's RBI single, which drove home Billy Hamilton, who reached base and scored in the first inning for the fourth straight game.

Ronald Torreyes, playing second base in place of resting Starlin Castro, singled and later scored on Aaron Hicks' second straight single to push the Yankees' lead back to 4-1.

Tanaka worked out of a bases-loaded, no-outs jam in the fourth to help New York maintain its lead.

"I was able to keep my poise," Tanaka said, via a translator. "It was a long game last night. I did have that in my mind to rest the bullpen."

NOTES: Monday was a scheduled day off for Yankees RF Aaron Judge, who entered the day tied with the Nationals' Ryan Zimmerman for the major league home run lead with 13. Aaron Hicks played right field. ... New York recalled RHP Chad Green from Triple-A Scranton/Wilkes-Barre prior to Monday's game and optioned INF Rob Refsnyder to the minors. ... Cincinnati is 7-9 all-time against the Yankees in five interleague series. ... Reds INF Arismendy Alcantara has hits in seven straight plate appearances after singling as a pinch hitter.