The Rangers have won six of eight games in Oakland this season and will go for their second three-game sweep at the Coliseum on Thursday afternoon.
The Rangers' ninth-inning rally came after Derek Holland pitched 6 1/3 innings but left trailing, 1-0.
"Those guys did a great job of picking me up," Holland said. "It was very awesome to watch. We have had a tough season to begin with, but the way we're finishing up strong, I'm very impressed with the way guys are carrying themselves. Nobody is quitting."
The Rangers still trailed going into the ninth after being held scoreless for eight innings by starter Jeff Samardzija. Closer Sean Doolittle took over not having allowed a run in his last 15 games. But the left-hander had also just been activated off the disabled list Friday after being sidelined with a strained rib-cage muscle.
"It was a tough game for us against Samardzija," Rangers manager Tim Bogar said. "He's a great pitcher and he had our number. But our guys never gave up."
Doolittle started out by getting Leonys Martin on a pop to right before Elvis Andrus singled. Rougned Odor followed with a double into the left-center-field gap, and Andrus raced around to score, beating shortstop Jed Lowrie's throw to the plate.
"I just don't think it was my night," Doolittle said. "I felt good. The ball Odor hit, give him credit, I thought it was a pretty good fastball away. He didn't try to pull it. He went with it the other way,"
Odor went to third and easily beat the throw from catcher Geovany Soto. Athletics manager Bob Melvin challenged the call because it appeared that Odor overslid and possibly stepped off the bag while third baseman Josh Donaldson was applying the tag. The safe call was upheld on review.
Adrian Beltre was then intentionally walked. Arencibia, who had struck out three times against Samardzija, fell behind 0-2 to Doolittle before hammering a 1-2 fastball over the left-field wall.
"When I got down 0-2, I thought, 'Let's go, you got to get this run in,'" Arencibia said. "This is an opportunity against a tough pitcher, we worked our way into this chance. I was looking for a ball down because he strikes out a lot of guys like that, and do something with it."
"I missed my spot a little bit, and he made me pay for it," Doolittle said.
Bogar said he considered pinch-hitting Luis Sardinas for Arencibia but decided against it.
"Sardinas is a contact guy, maybe squeeze or hit and run, stay out of the double play," Bogar said. "But I felt J.P. was a good matchup against Doolittle. Sometimes your stomach is smarter than your head."
The Rangers scratched out two more runs before the inning was over. The Rangers had six hits in the ninth after just four in eight innings against Samardzija.
Robbie Ross Jr. earned the victory as he and Phil Klein combined to keep it a 1-0 game by escaping a bases-loaded, no-out situation in the eighth. Klein retired Lowrie on a fly ball to shallow center then Ross got Alberto Callaspo on a popout and Soto on a fly ball.
"Obviously it has been an up-and-down year, so to have a little successful like that, I'm grateful," Ross said. "To get out of a jam like that and keep us in the game makes you feel good."