The Arizona rookie hit a tying homer off the big Texas right-hander in the eighth inning, then Cliff Pennington singled home the winning run in the ninth to give the Diamondbacks a 5-4 victory for a doubleheader sweep of the Rangers.
Darvish matched his career best with 14 strikeouts but allowed a run after the sixth inning for the first time this season.
"It was just that home run-mistake fastball that I made today," Darvish said through a translator. "It wasn't that bad of an outing for me."
Gregorius also had an RBI triple in the first.
In the opener, Tyler Skaggs struck out nine over six scoreless innings and the Diamondbacks held on to win 5-3.
"You can't look at it as a tough day. It's a fun day," Arizona manager Kirk Gibson said. "You get to play two games. You get to play a great team in the Rangers. It's a great measuring stick for us."
Pennington also had the winning hit in a 16-inning victory over St. Louis earlier this season.
After giving up two runs in the first, Darvish was in complete control until Wil Nieves led off the eighth with a pinch-hit single. Cody Ross struck out, then Gregorius lashed a 2-0 pitch over the fence in right field to tie it at 4.
"He threw me a low cutter and I put good wood on it," Gregorius said, "and it was like a line drive and it went out."
Darvish had dominated with his cut fastball and did not hesitate to use it again.
"I had to get a strike in there. I didn't want a 3-0 count," Darvish said. "I tried to hit the corner but he hit it pretty well."
Darvish, in just the second no-decision in his 11 starts this season, gave up seven hits but did not walk a batter. All three of his 14-strikeout performances have come this year. He is the first pitcher since Arizona's Randy Johnson in 2004 to have three games with at least 14 strikeouts in one season.
"Baseball's not a competition about getting strikeouts," Darvish said. "It's about winning."
Darvish pitched well, Texas manager Ron Washington said.
"It's just unfortunate that one pitch made the difference in the ballgame late," Washington said.
Miguel Montero led off the ninth with a double against Frasor. With one out, Robbie Ross walked pinch-hitter Martin Prado intentionally. That brought up the usually light-hitting Pennington, who sliced one down the right-field line to score Montero from second and give Arizona the comeback victory.
"Every player wants to do it anytime," Pennington said, "but when you are not swinging that bat as well as you want to swing it, it feels even better."
Trevor Cahill gave up four runs, three earned, and seven hits in eight innings for Arizona.
On Darvish's first two pitches of the game, Gerardo Parra singled, then Gregorius tripled down the right-field line to make it 1-0. Gregorius just beat left fielder David Murphy's throw on Eric Chavez's sacrifice fly for Arizona's second opening-inning run.
The Rangers tied it with an unearned run in the fourth. Singles by Lance Berkman and Pierzynski put runners at first and second with one out. Craig Gentry bounced to third for what could have been an inning-ending double play, but Pennington's relay throw was wild. Berkman scored on the play to knot it at 2.
Texas took the lead with two runs in the sixth. Berkman drew a one-out walk and Beltre singled. Pierzynski's single brought home the go-ahead run, then Beltre scored when Gentry grounded into a fielder's choice to put Texas up 4-2.
Skaggs (1-0), who lost out to Patrick Corbin for Arizona's fifth starting spot in the spring, was recalled from Triple-A Reno after scheduled starter Ian Kennedy cut his right index finger washing dishes.
"It was kind of a late-notice thing," Skaggs said. "I'm happy that they called me up and had the confidence in me to actually start the ballgame. So hopefully I opened up a few eyes."
He gave up three hits and walked three, one intentionally, mixing in his nasty curveball with an effective fastball and changeup in his first major league victory since he won his big league debut last year.
Another 21-year-old lefty, Martin Perez (0-1), took the loss in his first start of the season, allowing four runs, three earned, in 5 1/3 innings.
Cody Ross hit a solo homer for the Diamondbacks. Beltre had a two-run single in Texas' three-run ninth.
The Rangers had to play a doubleheader on the heels of a 4-3, 13-inning loss at Seattle on Sunday. They struck out 15 times in Monday's opener, a season high for Texas batters and Arizona pitchers.
A.J. Pollock and Eric Hinske each doubled in a run. Prado had an RBI single, tying a franchise record in the process with his seventh consecutive base hit. Paul Goldschmidt also singled in a run for Arizona.
The teams play each other four straight times, the next two at Texas on Wednesday and Thursday. ... Parra left the nightcap in the fifth inning with a strained left calf. ... Goldschmidt has 40 RBIs. ... Five Diamondbacks have had hits in seven consecutive at-bats, the most recent being Eric Byrnes in June 2007.