The Rangers have now won six straight, their longest winning streak of the season and the longest current streak in the Majors.
"You always want to play well and finish on a great note," Adrian Beltre said. "It's just nice that we're playing really good baseball."
During the winning streak, the Rangers are hitting .310, including .379 with runners in scoring position. Their pitchers have a 2.00 ERA with opponents hitting .217 off them. They have committed just four errors defensively.
"We're playing well together," infielder Adam Rosales said. "We have good team chemistry. We're all excited to show up to the field and compete. We have a lot of young guys and they bring energy. They're playing well. These are good teams we're beating. But our team can beat any team if we play the way we're capable of playing."
The Athletics were hoping right-hander Sonny Gray, who was 3-1 with a 1.82 ERA against the Rangers this season, could prevent the sweep. But the Rangers scored four runs in the first inning off him after just six runs in 29 2/3 innings over the four previous outings.
But some of those other lineups didn't have Jake Smolinski and Ryan Rua in them. Smolinski, making a mockery of pitchers on his rehab assignments, was 4-for-5 on the afternoon and is 6-for-13 since coming off the disabled list without having played in a game in six weeks. Rua was 2-for-4, including the final of four straight two-out singles in the first inning against Gray.
The Rangers had 15 hits, and they had five rookies in the lineup combine to go 9-for-22.
"They are getting some serious time under their belts and getting some at-bats and seeing what they can do," manager Tim Bogar said. "There have been a lot of positives to look at."
Rangers starter Nick Martinez earned the victory by holding the Athletics to two runs on three hits, three walks and two strikeouts in 5 2/3 innings. It was his first win since Aug. 20 against the Marlins, and he is now 4-11 with a 4.85 ERA on the season.
"Every win is big for a starter, especially when they have been a little scarce this year," Martinez said. "I did a good job today of getting some quick outs, and getting some quick innings and getting the team back in the dugout."
Elvis Andrus got the Rangers started with a one-out single, and was forced out at second on Rougned Odor's grounder. Texas then came up with four straight singles by Beltre, Smolinski, Tomas Telis and Rua to take a 3-0 lead. Telis scored the fourth run of the inning on catcher Derek Norris' passed ball.
"Left some pitches up and they jumped on them and put good swings on them," Gray said. "Unfortunately for us, I just dug us in a hole a little bit too deep. If you give up four in the first, nine times out of 10 you're not going to recover."
Martinez walked two in the third and Sam Fuld responded with a two-out triple. But that was all the A's would score. The Rangers added one in the fifth as Beltre walked, went to third on Smolinski's single and scored on Telis' fielder's choice.
In the sixth, after Dan Otero relieved Gray, Rosales singled and scored on a double by Leonys Martin. A single by Andrus drove home Martin, and now the Rangers juggernaut rolls on to Anaheim for a three-game series with the Angels.