Texas' loss keeps the Rangers seven games behind Boston in the AL wild card, and it clinched a postseason berth for the New York Yankees.
Suzuki hit a two-run double and scored on Barton's RBI single during a five-run seventh when the A's broke the game open to win for the 10th time in 12 games.
Oakland improved to 14-6 in September, tied with Colorado for the best record in the majors. It's the first time since June 2008 the A's have had a winning record in a month.
David Murphy had two hits and an RBI while Ivan Rodriguez singled twice for the Rangers, who lost for the eighth time in 11 games.
Texas carried a four-game road winning streak into the game and had scored at least 10 runs in each of the four victories, one shy of the major league record. But the Rangers weren't able to get much going against Cahill, Oakland's baby-faced rookie.
In addition to extending his career-best winning streak to four games, Cahill improved to 3-1 against the Rangers and hasn't lost to any team since falling to Baltimore on Aug. 11.
The A's right-hander scattered six hits and gave up one run over 5 2/3 innings with two walks and one strikeout to become Oakland's second 10-game winner this season. Cahill (10-12) retired the first seven batters and got some help from Oakland's defense, which turned double plays in three straight innings and four overall.
Jack Cust walked with one out in the fifth and scored when Nelson Cruz misplayed Barton's sinking liner into a triple. Barton was running to third when the relay throw home from Texas second baseman Ian Kinsler skipped past catcher Rodriguez for an error, so Barton kept going and scored to make it 2-0.
The A's added another run in the fourth on Barton's RBI single then broke it open in the seventh with five straight hits and six overall. Rajai Davis had an RBI single to start the inning, Suzuki and Cust added run-scoring doubles and Mark Ellis also knocked in a run to give the A's a seven-run lead.
Craig Breslow, Jerry Blevins and Brad Ziegler completed the seven-hitter for Oakland.
Texas starter Brandon McCarthy (7-4) pitched effectively but lost for only the second time in his last six decisions. Both losses have come against Oakland, which has won eight of the last 10 games between the teams.
The Rangers' right-hander gave up five hits but was done in by Kinsler's throwing error in the second and by Texas' offense which went 1 for 7 with runners in scoring position.
Notes
Oakland is 5-1 on its current homestand. … The A's won despite leadoff hitter Adam Kennedy getting ejected in the first inning for arguing with home plate umpire Eric Cooper after being called out on strikes. It was the fifth ejection of Kennedy's career, his first since 2006. … Texas rookie SS Elvis Andrus went 1 for 4 and is batting .298 over his last 51 games.