Darvish retired his first 15 batters before Matt Dominguez singled softly to center, one pitch after Alex Rios nearly caught Dominguez's foul into the right-field corner before running into the padded wall as the ball landed.
Darvish came within one out of a perfect game in Houston on April 2 last year, when Marvin Gonzalez grounded a single between the pitcher's legs. He held the Astros hitless in Houston last Aug. 12 before Carlos Corporan's one-out homer in the eighth.
''It's sheer luck,'' Darvish said through an interpreter. ''But if I could pitch like this in every game, it would be very nice.''
Darvish allowed just the one hit and one walk in eight innings with nine strikeouts. He fanned five consecutive batters in the third and fourth innings all swinging. Darvish said he didn't realize he was pitching a no-hitter.
''I was only focused on not giving up runs, so it really didn't matter to me,'' he said.
Darvish pitched despite bleeding from the knuckle of his right thumb in the middle innings. He said that happened to him multiple times when he pitched in Japan and has never affected his control.
''When he left the game,'' Astros manager Bo Porter said, ''we just thought, `Let's take our shot at somebody else.'''
But the Texas' bullpen limited Houston one more hit and two walks, completing a two-hitter.
Darvish hasn't allowed a run in 15 innings through two starts. Rangers manager Ron Washington said he sees a crisper Darvish than the one who led the major leagues in strikeouts last season.
''In a way, he's just saying he can do anything that he wants to do with that baseball,'' Washington said.
Former President George W. Bush - a former Rangers' owner - watched with Hall of Fame pitcher Nolan Ryan, who quit as Texas' controlling owner last October and became executive adviser of the Astros.
Texas was 0 for 14 with runners in scoring position and had stranded 15 runners before Chirinos' hit off Brad Peacock (0-1). The Rangers loaded the bases with no outs in ther 10th.
''I don't get frustrated,'' Texas manager Ron Washington said. ''When you get frustrated, you're blind to what's going on.''
Kevin Kouzmanoff singled with one out, advanced on a wild pitch and scored on Chirinos' hit to center, ending the game after 4 hours, 11 minutes. Texas left the field with its third straight walkoff win.
Jason Frasor (1-0) worked a hitless inning for the victory.
Astros starter Scott Feldman, pitching two days after his 70-year-old father died, allowed two hits in seven innings.
''I knew without a doubt he would want me to pitch,'' said Feldman, a former Ranger pitching for the first time as a visitor in Arlington. ''I had to go out and keep my emotions in check. I think he was watching. He was a big baseball fan. I knew he would want me to do a good job.''
NOTES: Rangers RHP Colby Lewis, who hasn't pitched since July 2012 because of arm and hip injuries, is scheduled to start early next week. ... Astros RHP Matt Albers returned from paternity leave on Friday. His wife, Tara, delivered their first child, Mason James. ... The Rangers returned RHP Seth Rosin to the Philadelphia Phillies, who assigned him to Triple-A Lehigh Valley. Rosin (1-0) was taken by the New York Mets in the winter meeting draft, traded to the Los Angeles Dodgers and traded to Texas on March 26.