ARLINGTON, Texas -- In front of his parents and not far from his hometown, New York Yankees starter Nathan Eovaldi flirted with history Monday night.

Eovaldi took a no-hitter into the seventh and shut down the Texas Rangers in the Yankees' 3-1 win Monday night at Globe Life Park.

Eovaldi was backed by home runs from Jacoby Ellsbury and Starlin Castro as the Yankees opened a nine-game road trip. New York (8-10) has won three of its last four games.

The Rangers (10-10) have dropped their last four games, but remain tied for first in the American League West with Oakland.

Texas was without ace Cole Hamels, who missed his scheduled start with left groin soreness. It probably didn't matter the way Eovaldi (1-2) was slinging it.

The 26-year-old right-hander from Alvin, Texas, had it all working against the Rangers in his longest outing of the season. Eovaldi struck out six and gave up just two hits before exiting after walking the leadoff batter in the eighth.

"They've got a lot of early swingers, and I was just trying to locate the ball in and away and locate the offspeed pitches and be careful with it," Eovaldi said. "I feel like I've gotten better each outing. For it all to come together tonight, it was nice."

Eovaldi fell one strikeout short of breaking the club record of eight consecutive games with at least seven punch outs.

The Rangers didn't get a hit until rookie Nomar Mazara slapped a single through a shift on the left side to open the seventh.

"When it was hit, I thought it was an out," Eovaldi said.

Mazara was promptly erased by a double play.

Eovaldi had multiple pitches working, including his fastball, split-finger fastball, changeup and slider.

"He was amazing," said Texas first baseman Prince Fielder, who had one of Texas' two hits. "His split was what, 90? Anything that started at your thigh went straight to the ground. If you can get a big league team to go no-hit into the seventh, you're doing something good."

Yankees reliever Dellin Betances hadn't been scored upon this season until Texas catcher Brett Nicholas recorded his first major-league home run in the eighth.

New York closer Andrew Miller set the Rangers down in order in the ninth for his fifth save in as many chances.

Texas has scored only five runs during its four-game skid.

"I believe this offense will get going," Rangers manager Jeff Banister said.

Texas lefty Cesar Ramos, called up from Triple-A, was solid in his spot start in place of Hamels. Making his first major-league start in nearly two years, Ramos (0-1) allowed three runs in six innings despite giving up nine hits and three walks.

"I was just trying to go deep into the game and tried to do my part," Ramos said. "It worked out great, and I got to at least pitch into the seventh."

Ellsbury, Castro, Mark Teixeira and Austin Romine each had two hits for New York. Castro's third homer of the season made it 3-0 in the sixth.

The Yankees touched up Ramos for two runs in the third. Ellsbury hit his first home run of the season to lead off the inning. Teixeira's one-out double down to deep right-center scored Carlos Beltran from first.

Ellsbury's blast marked the 15th time in 18 games that New York held a lead at some point in the contest.

Ramos escaped a based-loaded, one-out jam in the second with a pair of infield ground balls.

Eovaldi was filthy early. The hard-thrower kept the Rangers off balance, allowing only two baserunners through six innings without a hit. Texas reached on an error in the second and walk in the fourth.

NOTES: New York DH Alex Rodriguez (oblique) was out of the lineup Monday. He left Sunday's game against Tampa Bay after experiencing stiffness. MRI results were negative, and Rodriguez traveled with the team to Texas. Manager Joe Girardi would be surprised if Rodriguez had to go on the disabled list. "It's not ideal, but it's not going to be for a long period of time," Girardi said of A-Rod's absence. ... Texas purchased the contract of LHP Cesar Ramos from Triple-A Round Rock for his start Monday against the Yankees. In corresponding moves, RHP Nick Martinez was optioned to Round Rock, and RHP Keone Kela was transferred from the 15-day DL to the 60-day DL. Kela is expected to miss three months after having a bone chip surgically removed from his right elbow Friday. ... The Yankees acquired LHP Phil Coke from the independent Atlantic League. Coke will report to Triple-A Scranton/Wilkes-Barre.