Hosmer hit a three-run homer as the Royals batted around in a five-run third that included consecutive triples by Billy Butler and Alex Gordon.
''You've got to love Arizona,'' Hosmer said. ''That's about 30 percent my power and 70 percent Arizona. I got a good piece of it, but Arizona might have helped it out a little bit. You want to work good at-bats and as a team I think we did that today, so it was productive.''
Perez went 3 for 3, with a home run in the second, RBI double in the third and a run-scoring single in the fifth.
Ryan Ludwick and Todd Frazier hit back-to-back homers as the Reds batted in a four-run first off left-hander Danny Duffy. The Royals committed two errors in the inning, and Duffy had a wild pitch and hit a batter.
Reds: Cueto, who won 19 games in 2012 but was restricted to 11 starts last year after three stints on the disabled list with a strained right latissimus dorsi muscle, threw eight pitches in a flawless first. He struck out four of his first nine batters, then allowing four consecutive extra-base hits with two out in the third inning. He allowed six runs and threw 58 pitches in 2 2-3 innings.
''The first two innings were more like the Johnny we're used to seeing,'' Reds manager Bryan Price said. ''He did a lot of things we like to see. We would have liked to have had a better result in the third.''
Royals: Duffy, trying to earn a rotation slot, threw 31 pitches in the first but only nine in a perfect second. He also took a Chris Heisey line drive off his right shin that caromed to Hosmer at first.
''I'm putting a lot of pressure on myself, trying to make this team,'' Duffy said. ''With the numbers I put up today, it's never good. But 95 percent of the time, if I throw the way I did today I'm going to put up zeroes. The first inning I thought I threw just as well as I did my second inning.''
Bill Duplissea and Cody Clark will be the Royals' replay coordinators. Duplissea has been the Royals bullpen catcher the past eight years. Clark, 32, was a catcher in the Royals' farm system from 2007-12. He made his major league debut last season with Houston, striking out 15 times in 38 at-bats with only four hits. The game Wednesday against the Diamondbacks will be the first of five Royals' spring training games where the replay challenge will be tested.
Royals: Second baseman Omar Infante, who has missed five games with a sore right shoulder, will likely be a designated hitter Wednesday. Right-hander Louis Coleman, who has yet to pitch because of a bruised right finger, threw batting practice with no problems.
Reds: Right-hander Mat Latos, who underwent arthroscopic left knee surgery last month, is to throw his first bullpen session Wednesday.
Royals shortstop Alcides Escobar, who has been on a paternity leave and has yet to play this season, is back.
''We'll give him a day or two to get his feet back on the ground and get going,'' Royals manager Ned Yost said.