Jonathan Lucroy's solo homer in the fourth got the Rangers on the board, but their two-run fifth was more the result of a methodical approach.
Elvis Andrus led off the inning with a single off A's starter Sean Manaea. After Drew Stubbs struck out, Delino DeShields lined a ball toward center fielder Jake Smolinski and didn't hesitate, taking second base on an aggressive play.
"When I hit the ball in the gaps, I always think [triple] -- that's just how I've always been my whole life," DeShields said. "I always round really hard, and if I feel good about it, I take a chance on it."
DeShields' double set up Ian Desmond, who followed with a two-run single to give the Rangers a lead they'd keep the rest of the night in support of starter Yu Darvish.
"Offensively, it's what our club does. They chip away, move the line and put together at-bats," Banister said. "They don't get too big with their swings, and when we do that, I think we're a premier offense."
The Rangers didn't score in the sixth but were back at it again with their aggressive play on the basepaths in the seventh. Andrus again led off with a single. Stubbs followed with a bunt single toward A's first baseman Yonder Alonso, but second baseman Max Muncy didn't cover first.
With DeShields at the plate, and with a 3-0 count, the Rangers pulled off a double steal, started by a huge jump from Andrus at second.
"Elvis is a veteran guy. He knew what he saw. With that count, the pitcher's not really paying attention to the people on base," said DeShields, who walked on the following pitch. "They just want to get a strike over, so we took advantage of that."
Desmond drove in another run with a single, and it looked as though that was all the Rangers would get in the inning when Carlos Beltran grounded into a 4-2-3 double play. But Lucroy came through again with a two-run double down the right-field line to give him three RBIs after the A's elected to intentionally walk Adrian Beltre in front of him.
"We had good at-bats all up and down the lineup -- a lot of big hits," Lucroy said. "[Desmond] had a couple of big hits there. When you have a lot of traffic on the bases, it just creates opportunities to score runs. It was a lot of fun to be in that lineup tonight."
Ryan Posner is a reporter for MLB.com based in Texas.