Phillips, who was stationed at second base to start the 10th inning under rules installed for the 2020 season, advanced to third on a bunt from Erick Mejia. Phillips came around to score after Franco's sacrifice fly to deep center field off James Karinchak (0-1).
Scott Barlow (1-0) was credited with the win after striking out back-to-back batters with the bases loaded in the ninth inning. Greg Holland fanned three in a row in the 10th to secure his first save of the season for the Royals, who won their first game under new manager Mike Matheny.
Jorge Soler and Salvador Perez belted back-to-back homers in the first, and Brady Singer tossed five strong innings in his major league debut. Singer, who was the 18th overall pick in the 2018 MLB Draft, settled for a no-decision after permitting two runs on three hits with seven strikeouts.
Mike Clevinger, who entered the game with a 9-0 record and 1.93 ERA in 13 career appearances versus Kansas City, overcame a sluggish start in the first before shutting down the Royals over the next six innings. The 29-year-old allowed just those two runs on four hits and retired the final 10 batters he faced.
Kansas City got the early jump on Clevinger and the Indians, with Soler depositing a 3-2 slider over the high wall in left field to open the scoring. Soler's homer was his first of the season after he went deep an American League-best 48 times in 2019.
Perez doubled the advantage in short order by sending an 0-1 fastball into the bleachers in center field.
Cleveland answered in the third inning as Jose Ramirez's single to shallow right plated Bradley Zimmer before Cesar Hernandez scored on a wild pitch.
Prior to the game, the Indians placed outfielder Tyler Naquin on the 10-day injured list because of a hairline fracture of a toe on his right foot. The team recalled right-hander Zach Plesac to take his place on the 30-man active roster.
--Field Level Media