Gallo's home run, his team leading 16th of the season, sailed 457 feet and landed in the second seating area beyond the center-field wall.
Ariel Jurado (2-2) won for the first time in three major league starts this season. Jurado allowed two runs on five hits and three walks. The second-year right-hander, who was recalled from Triple-A Nashville on April 26, had career highs in strikeouts (six) and pitches (101).
Danny Duffy (3-2) lost for the first time since April 26. Carrying a two-hit shutout into the sixth inning, Duffy allowed all six runs, six hits and two walks -- both in the sixth.
Jesse Chavez, the first of three Texas relievers, worked a 1-2-3 seventh inning. He ran his scoreless streak to 17 1/3 innings in May, a franchise record for one month.
Texas loaded the bases in the sixth inning on outfield singles by Shin-Soo Chooand Elvis Andrus and a chopper hit between third base and the mound by Hunter Pence. Duffy fielded Pence's grounder, but his throw to first base was late.
Duffy walked Nomar Mazara with the bases loaded to tie the score 2-2. Gallo then launched a 1-1 fastball to end a six-game homerless streak, which matched his longest this season.
Cheslor Cuthbert homered in his first major league at-bat of the season, and Alex Gordon tripled-in Kansas City's other run. Cuthbert, who earlier Friday had his contract selected from Triple-A Omaha, hit an opposite-field homer that just cleared the right-field wall in the second.
Gordon's triple in the fifth inning turned around centerfielder Gallo and struck about midway up the wall in straightaway center, scoring Adalberto Mondesi. In the third inning, Gallo broke in on a fly ball hit by Whit Merrifield that went over his head for a triple.
The Royals lead the majors with 24 triples.
Mondesi had his major league-leading 19th stolen base. That gave the Royals a major league-leading 53.
To make room for Cuthbert, the Royals designated INF-OF Chris Owings for assignment. The Rangers selected the contract of RHP David Carpenter from Nashville and optioned OF Zack Granite to Nashville.
Royals: OF Hunter Dozier (right thorax tightness) is day to day, leaving Thursday's game in the fifth inning and sitting out Friday.
Rangers: OF Willie Calhoun (left quad strain) will begin on-field work on Saturday.
Rangers: RHP Lance Lynn (6-3, 4.67) has lowered his ERA from 6.51 over his last six starts, going 4-2.