Gallo hit his ninth homer of the season and Kiner-Falefa hit his second off Nick Goody (0-2), who entered with two outs in the 10th inning.
Nomar Mazara and Delino DeShields also homered for the Rangers, who won for the fourth time in six games.
Michael Brantley brought Cleveland all the way back from a 6-0 deficit when he hit a two-out grand slam off Texas right-hander Keone Kela in the ninth inning after Tyler Naquin opened the inning with a single and Francisco Lindor and Jason Kipnis singled with one out to load the bases.
The Rangers failed to turn a double play after Naquin's single when shortstop Jurickson Profar made an off-target throw to second base on Bradley Zimmer's grounder. Brantley hit an 0-2 pitch for his first grand slam of his career.
Left-hander Alex Claudio (1-1) pitched three innings for his first win of the season.
Kipnis had two hits including a two-run double in the seventh inning and Yan Gomes, Lindor, Edwin Encarnacion and Jose Ramirez had two hits apiece for Cleveland, which has lost four of six.
Profar had two doubles and drove in three runs, Kiner-Falefa had four hits and DeShields had two hits for the Rangers.
DeShields hit his first homer of the season with two outs in the fifth inning to break a scoreless tie, and Mazara hit a two-run homer to cap a four-run seventh inning as the Rangers took a 6-0 lead.
Rangers starter Doug Fister gave up six hits and two unearned runs in 6 2/3 innings while striking out four and walking two.
Cleveland starter Mike Clevinger gave up seven hits and three runs in 6 2/3 innings, striking out seven and walking one.
--Field Level Media
Texas | Cleveland | |
Doug Fister | Player | Mike Clevinger |
No Decision | W/L | No Decision |
6.2 | IP | 6.2 |
4 | Strikeouts | 7 |
6 | Hits | 7 |
0.00 | ERA | 4.05 |
Texas | Cleveland | |
Isiah Kiner-Falefa | Player | Edwin Encarnacion |
4 | Hits | 2 |
1 | RBI | 0 |
1 | HR | 0 |
8 | TB | 2 |
.667 | Avg | .400 |