Gray (4-1) allowed only three singles while striking out six. Texas got only one runner to third base against the right-hander, who threw two wild pitches in the sixth after Robinson Chirinos singled.
Darvish (1-1) was gone after 3 1-3 innings, pulled after walking No. 9 batter Eric Sogard for the second time. Those were the only two walks for the right-hander, who allowed four runs and six hits while throwing 83 pitches (45 strikes). Darvish is winless his last nine home starts.
Josh Donaldson had a two-run single in the third, and the A's made it 4-0 an inning later when Josh Reddick had an RBI triple before coming home on Daric Barton's sacrifice fly.
Gray, in his 16th career start, threw 73 of his 108 pitches for strikes.
Oakland and Texas entered tied for the AL West lead and the league's best record at 15-10. The Rangers, shut out for the first time this season, had swept a three-game series in Oakland last week.
Darvish made his 66th start for the Rangers since signing with them from Japan before the 2012 season. His shortest previous MLB outing had been four innings at Seattle on May 21, 2012, and he had since gone at least five innings in 56 consecutive starts. Darvish did have a start of only 1 1-3 innings in Japan eight years ago.
Darvish struck out four, but three of those came in the first five batters of the game.
Gray walked Rangers leadoff hitter Michael Choice to get his night started, but got out of the first with a fielder's choice grounder and then a 4-5-3 double play with three Oakland infielders shifted to right side against Prince Fielder.
Choice grounded into an inning-ending double play in the third after the bottom two batters reached base.
The A's are 7-1 in their nine games against Darvish, who last week got a no-decision in Oakland after going six innings and leaving a 3-3 tie. The Rangers won that game 4-3.
After Donaldson's big hit, a bouncer through the left side of the infield out of the reach of diving third baseman Adrian Beltre, the A's had the bases reloaded on a one-out single by Brandon Moss.
Moss was thrown out retreating to first on a pitch that got away from catcher Chirinos, though the runner was originally ruled safe before Rangers manager Ron Washington challenged and got the play overturned by replay. When Moss slid back in, his foot was against first baseman Fielder's foot — and not the base — while being tagged.
Washington lost a challenge in the eighth when thought Reddick was out on a pickoff attempt diving back to first with Barton batting. Reddick was called safe, and replay confirmed the call before Barton hit a deep flyball.
Center fielder Leonys Martin made a leaping catch on the warning back and threw to first base. Reddick was initially called safe by crew chief Jeff Nelson, who then initiated a replay and changed his call for an inning-ending double play.
NOTES: Rangers OF Shin-Soo Choo was out of the starting lineup for the sixth consecutive game because of a left ankle sprain, but flew out as a pinch-hitter in the ninth. ... A's OF Yoenis Cespedes missed his fourth game in a row (strained left hamstring). Manager Bob Melvin is hopeful he will be back in the starting lineup Tuesday. ... Game 2 features a standout matchup of left-handers. Oakland's Scott Kazmir (3-0, 1.62 ERA) pitches against Martin Perez (4-0, 1.42), who has thrown 26 consecutive scoreless innings his last three starts. Perez has two consecutive three-hit shutouts, the last coming Wednesday in Oakland.