ARLINGTON, Texas -- Cleveland Indians right-hander Carlos Carrasco is proof that spring training numbers mean nothing.

Carrasco was awful in the spring, posting a 10.80 ERA and fighting through right elbow inflammation.

But Tuesday's game really counted, and Carrasco delivered as the Indians edged the Texas Rangers 4-3 behind the right-hander's pitching and some nifty work by the bullpen.

Cleveland is now 2-0, while the Rangers are off to their first 0-2 start since 2007.

Carrasco (1-0) allowed two runs on four hits over 5 2/3 innings, striking out seven and walking just one.

"Every inning I got stronger, more comfortable with my pitches," Carrasco said. "It felt great to be back. This year is a new year, so I feel pretty good for myself with my body, with my arm. Everything's fine."

Carrasco wasn't perfect, but he didn't need to be as the Indians gave him early runs off Texas lefty Martin Perez (0-1).

First baseman Carlos Santana started a big night for him by leading off the game with a solo homer. An inning later, he helped push the lead to 3-0 as he followed an RBI single by Austin Jackson with one of his own.

The Rangers cut the lead to 3-2 in the bottom of the second when Joey Gallo blasted a two-run homer to right. It was just the second hit in 29 at-bats for Gallo with the Rangers over the last two seasons, with both being homers.

Perez allowed three runs in six innings, walking four and striking out four. After allowing four hits in the first three innings, he gave up just one over his final three.

"They (the Rangers' defense) made good plays and I started to pitch my game," Perez said of his adjustments. "In the second inning I was thinking too much and I was walking a lot on the mound. After they made a play, I decided I'm going to throw my game, do it quick and not think too much and 'Let's pitch. Let's throw the ball where (catcher Robinson) Chirinos calls it. After that I had good results."

The adjustments Perez made are a cause for hope for Texas, but the staff's pitching the first two games has been erratic. Texas pitchers have already walked 11 batters.

"It was encouraging to see him settle down," Texas manager Jeff Banister said of Perez. "Obviously we're getting to a point where it's time to put that together throughout an entire game. I'm sure if you ask him it's not how he would want to start the game, falling behind and walking. What I do know is that we've had 11 walks in the first two games and we've got to calm that down. We've got to limit that."

Cleveland gave Carrasco some much-needed insurance in the seventh inning on an RBI single from Michael Brantley off Texas lefty Dario Alvarez.

The Indians needed that run because after 2 1/3 scoreless innings from the bullpen, Texas had a chance in the ninth. First baseman Mike Napoli lined a double off to wall in center to make it a one-run game, but Cody Allen came back and struck out Rougned Odor, Jurickson Profar and Gallo with the tying run at second.

Allen emerged with his second save.

Cleveland manager Terry Francona had faith Allen would finish the Rangers.

"I thought Cody threw the ball really well, just maybe too many strikes," Francona said. "But you could tell what kind of stuff he had because after those first two hits, man, he really threw. There was no wiggle room, and he didn't need it."

Cleveland's bullpen has allowed just one run in 6 1/3 innings of work in the series.

The Indians had seven hits, with Santana, Brantley and Jackson each accounting for two of them. Outfielder Nomar Mazara and Gallo each had two hits for Texas.

NOTES: Texas RHP Keone Kela, who was optioned to Triple-A before the season because of his clubhouse behavior, has been given an extra day to report to Round Rock. He's slated to report Wednesday. The four-run deficit overcome by the Indians Monday marked just the fourth time in club history Cleveland has overcome a deficit of at least four runs to win a season opener dating back to 1901. ... Cleveland OF Lonnie Chisenhall (right shoulder sprain) will begin a rehab assignment Friday with Triple-A Columbus and could be ready for the home opener next Tuesday.