Brown hit a three-run homer and drove in four runs to help the Athletics beat Texas 12-6, ending the Rangers' season-best five-game winning streak Sunday.
"I'm not a walk guy," Brown said. "I'm just ready to hack."
The A's pulled off two double-steals, hit early in the count and took advantage of eight walks and two errors to lift an offense that had scored three runs or less in seven of their previous 11 games.
Ian Kinsler had three hits for the Rangers, who had won nine of their previous 11.
With the game tied at 6, Bobby Crosby led off the seventh with a double, then stopped at third on Ellis' single. Rangers reliever Franklyn German's pickoff attempt had Ellis in a rundown between first and second, but when Crosby broke for the plate, Rangers first baseman Frank Catalanotto threw late to catcher Jarrod Saltalamacchia as Crosby scored to put the A's in front.
"We got a little lucky," A's manager Bob Geren said. "They got us and we got away with it."
Rangers manager Ron Washington said his team worked on defending the double steal in spring training, "but we didn't execute. They beat us in execution."
Ryan Sweeney added a sacrifice fly later in the seventh to extend Oakland's lead to 8-6, and Brown's RBI single in the eighth made it 9-6.
Daric Barton added a two-run homer in the ninth for Oakland.
German (1-1) gave up two runs and three hits in 2/3 inning to pick up the loss.
Santiago Casilla (2-0) allowed two hits in 1 1/3 innings for the victory.
Rangers starter Sidney Ponson allowed six runs and seven hits in 5 1/3 innings, his worst outing of the four starts since his contract was purchased from Triple-A Oklahoma on April 26.
The A's activated Rich Harden from the 15-day disabled list to make his first start since April 2, but he couldn't hold a four-run first-inning lead. Harden was placed on the 15-day disabled list April 10 with a strained right shoulder.
In the first, Thomas' RBI single and Brown's fourth homer of the season gave the A's a 4-0 advantage.
Ponson tried to throw a sinker down and away to Brown but left the pitch over the plate.
"I didn't have any command of any pitch today," Ponson said. "It's one of those days where you know you don't have anything, you just try to mix your pitches and they hit the ball on the ground. But they didn't do that at all today. It was a souvenir. He did what he's supposed to do."
Saltalamacchia's two-run single in a four-run third tied it for the Rangers, who took a 5-4 edge in the fourth on Josh Hamilton's RBI triple.
Harden allowed five runs and eight hits in 3 2/3 innings.
"First time out, I'm somewhat happy," said Harden, who's been on the disabled list six times in the last four years. "Obviously I didn't get that many innings in and gave up some runs, but I wasn't disappointed. The second and third innings went by so quick, I didn't get much of a rest."
Ponson walked Jack Cust with the bases loaded in the sixth as the A's tied it at 5, and Thomas followed with a sacrifice fly off German to give Oakland the lead.
To open a roster spot for Harden, OF Chris Denorfia went on the 15-day DL because of tightness in his lower back. ...Texas placed RHP and No. 1 starter Kevin Millwood on the 15-day disabled list due to a strained right groin. RHP Doug Mathis was called up from Triple-A Oklahoma to take Millwood's roster spot. Mathis, awaiting his major league debut, will begin in the bullpen but is a candidate to get a spot start on May 20, the next time there's an opening in the Texas rotation. ...Texas also outrighted RHP Kazuo Fukumori, currently with Oklahoma, off the 40-man roster. ...All of the Rangers and a few of the A's used pink bats in honor of Mother's Day and to promote breast cancer awareness. The teams combined to go 12-for-47 with the pink bats. ...The Rangers are 0-18 when trailing after seven innings. ... Ellis left the game in the ninth for a pinch runner after sustaining a minor hamstring strain. He's listed as day-to-day. ... A's 3B Eric Chavez will begin a rehab assignment at Triple-A Sacramento on Thursday. Chavez is on the 60-day DL after offseason back surgery.