Hosmer, a first baseman, connected for a three-run homer in the first inning off the rookie Cody Anderson (2-2) as the Royals rolled to their American League-leading 60th win and improved to 15-5 in their last 20 games.
Edinson Volquez (10-5) worked into the seventh inning for Kansas City, which will welcome newly acquired ace Johnny Cueto on Tuesday.
The rookie Francisco Lindor hit a three-run homer and Carlos Santana a solo shot for the Indians, who have dropped five straight.WHITE SOX 10, RED SOX 8 Adam Eaton had three hits and drove in two runs to propel visiting Chicago to its fifth straight win.
Boston’s David Ortiz homered for the third time in two games, hitting a two-run shot in the first inning after driving in a career-high seven runs in a win Sunday.
Earlier, the Red Sox traded Shane Victorino, a two-time World Series champion, and more than $3.8 million to the Angels for infielder Josh Rutledge. Victorino, 34, has hit .276 with 108 homers in 12 seasons.
RAYS 5, TIGERS 2 Curt Casali homered twice, Nathan Karns took a one-hit shutout into the seventh inning, and host Tampa Bay handed Detroit its seventh loss in 10 games.
Consecutive doubles by Steven Souza Jr. and Kevin Kiermaier made it 2-0 in the fourth, and Logan Forsythe had a two-out R.B.I. single off Anibal Sanchez (10-8) in the fifth.
Yoenis Cespedes led off the seventh with a home run, his 16th of the season, to pull the Tigers to 3-1; his single the next inning made it 3-2 before Casali hit his second homer to put the game out of reach.
CARDINALS 4, REDS 1 Kolten Wong hit a grand slam that proved to be all the offense St. Louis at home against Cincinnati.
Lance Lynn (8-5) allowed one run and five hits in seven innings.
The Reds loaded the bases in the third inning with no outs before Jay Bruce’s sacrifice fly. The next batter, Bryan Pena, grounded into a double play, ending their best scoring threat.