Cahill improved to 5-1 for his career against the Rangers, 2-0 with a 0.87 ERA in three starts at Rangers Ballpark, one of the toughest stadiums in the majors for pitchers.
But Cahill has no theories as to why he's so successful against a usually potent offensive team.
"I just try to keep the ball down and get lucky, I guess," Cahill said. "Just a coincidence."
Cahill (10-4) struck out four and walked three as he took over the team lead in victories, breaking a tie with Gio Gonzalez.
"[Cahill] threw only 90, 91 [mph] but he kept it off the fat part of the bat," Rangers manager Ron Washington said. "He was an All-Star for a reason. But our time will come."
Cahill was chosen for the AL All-Star team, but was ineligible because he pitched the Sunday before the game.
The Texas heat didn't deter Cahill, who threw 113 pitches. Neither did the fact that the wind was blowing out.
"You think about the environment he's pitching in, the weather, the team, that's about as good as you can do," A's manager Bob Geren said.
In pregame warmups, Cahill thought he had mediocre stuff.
"He just said, 'Oh, my gosh, it's going to be a long night,' " Suzuki said. "I just told him, 'Don't think about it, go out there and throw the ball.' "
Earlier in the day, the A's confirmed that right-hander Ben Sheets is out for the season due to a torn flexor in his right elbow.
The A's signed Sheets to a one-year, $10 million contract in January to pitch at the top of their rotation. Cahill has taken over that role.
"He's really kind of turned into our ace," Geren said.
Rajai Davis had three hits for the A's, who are 8-3 since the All-Star break. Oakland pulled within 7 1/2 games of the AL West-leading Rangers, moving past the Los Angeles Angels and into sole possession of second place for the first time since June 4.
Rangers starter Colby Lewis (9-7) matched Cahill until Suzuki's one-out homer in the sixth.
"It was one pitch, a hanging slider, and Suzuki hit it," Lewis said. "If I bury it, he's out."
Lewis went seven innings and 116 pitches, allowing one run and five hits with eight strikeouts and two walks.
Cruz went 1 for 4 to stretch his career-best hitting streak to 16 games.
Texas had runners at the corners with two outs in the fourth, but Cahill struck out Cruz looking to end the threat.
Texas committed three errors. ... Rangers 2B Ian Kinsler was rested. Kinsler's two-base error -- when he failed to cover second base on a steal attempt -- led to an unearned run for the A's in Tuesday night's game, Oakland's only run. Washington chalked it up to a "mental lapse," but said the miscue had nothing to do with the day off. ... Oakland has won five of six on the road. ... Cahill has gone at least six innings in eight straight starts. ... Suzuki has a team-high 12 homers.