The A's had a four-game winning streak snapped despite a two-run home run by Khris Davis, his seventh of the season.
The Rangers trailed 2-1 before Jurickson Profar ignited the fifth-inning rally with a two-out double. He scored the tying run on a single by Nomar Mazara.
After A's starter Kendall Graveman walked Joey Gallo, Kiner-Falefa came through with a single to right-center field, scoring Mazara with the eventual winning run.
Jesse Chavez, Alex Claudio and Chris Martin shut out the A's over the next three innings to retain the one-run lead before Ronald Guzman gave Rangers closer Keone Kela a two-run cushion with an RBI single that scored Kiner-Falefa in the eighth.
Kela recorded his fourth save with a 1-2-3 ninth, striking out two.
Chavez (1-0), who relieved starter Doug Fister with two outs in the fifth inning, threw 1 1/3 innings and was credited with the win.
All told, Chavez, Claudio, Martin and Kela faced 13 batters over the final 4 1/3 innings, and only one reached base. A throwing error by third baseman Kiner-Falefa put Marcus Semien on second to start the eighth inning against Martin.
However, Martin got hot-hitting Jed Lowrie to fly out to center field, which resulted in a double play when Delino DeShields threw out Semien trying to advance to third base.
Graveman (0-5) became the American League's first five-game loser, allowing three runs and six hits in six innings. He walked four and struck out seven.
Davis' homer came off Fister in the third inning. It followed a single by Semien and gave Oakland a 2-0 lead.
Juan Centeno's fielder's choice grounder scored Gallo, who had singled, to get the Rangers within 2-1 in the fourth.
Fister went 4 2/3 innings, allowing two runs on four hits. He walked three and struck out three.
Gallo went 3-for-3 and Guzman finished with a pair of hits for the Rangers, who completed a six-game homestand with a 2-4 record.
Semien had two of Oakland's four hits, a pair of singles, as the A's saw a three-game road win streak come to an end.
The Rangers out-hit the A's 8-4.
--Field Level Media
Oakland | Texas | |
Kendall Graveman | Player | Doug Fister |
Loss | W/L | No Decision |
6.0 | IP | 4.2 |
7 | Strikeouts | 3 |
6 | Hits | 4 |
4.50 | ERA | 3.86 |
Oakland | Texas | |
Marcus Semien | Player | Joey Gallo |
2 | Hits | 3 |
0 | RBI | 0 |
0 | HR | 0 |
2 | TB | 3 |
.500 | Avg | 1.000 |