ARLINGTON, Texas — Two-thirds of the way through Monday night’s game, the pitcher known around the Yankees as Nasty Nate made a more historically dramatic nickname seem a possibility:

No-Hitter Nate.

Nathan Eovaldi, with his usual high-90s fastball and the best splitter he’s had in a game since he’s been a Yankee, held the Rangers hitless for six innings.

Nomar Mazara ruined that bid with a leadoff groundball single to center in the seventh — and Prince Fielder added a double with two outs in the inning — but Eovaldi nonetheless helped the Yankees to an impressive 3-1 victory over the Rangers in front of 31,453 at Globe Life Park.

Before the seventh, the only hard-hit ball of note came off the bat of Adrian Beltre with one out in the fourth inning when he launched a fly ball to the warning track in left that Brett Gardner comfortably caught at the base of the wall.

Eovaldi walked Mitch Moreland to start the eighth and was replaced by Dellin Betances, who immediately induced a 6-6-3 double play off the bat of Elvis Andrus. Brett Nicholas, somewhat shockingly, followed with his first career homer, accounting for the first earned run allowed by Betances this season in 10 innings.

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Andrew Miller pitched a perfect ninth for his fifth save.

The Yankees (8-10), winners of three of their last four, caught a break earlier in the day when Texas lefthander Cole Hamels was scratched because of left groin soreness and was replaced by another lefthander, Cesar Ramos. Ramos, called up from Triple-A Round Rock to make the start, allowed three runs and nine hits, including solo homers by Jacoby Ellsbury and Starlin Castro.

The Yankees, who had 10 hits — two each by Ellsbury, Castro, Mark Teixeira and Austin Romine — were without Alex Rodriguez, who has an oblique injury, and Aaron Hicks, who has an injured left shoulder.

Joe Girardi said before the game that he doesn’t expect either injury to result in a stint on the disabled list.

“I feel good,” A-Rod said shortly after arriving at Globe Life Park Monday afternoon. “I feel ready to go.”

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That was a more than apt description for Eovaldi, who needed only nine pitches to get through the first inning and seven to get through the second, which included an error by Didi Gregorius that was erased by a double-play grounder.

Ellsbury gave the Yankees a 1-0 lead in the third, taking a 90-mph 3-and-1 fastball to deep right-center for his first homer of the season. Ramos walked Carlos Beltran and Teixeira jumped on an inviting 1-and-1 changeup, driving it to right-center for an RBI double that made it 2-0.

The Yankees put two runners on base for the third straight inning in the fourth as Gregorius and Romine singled with one out, but Ellsbury hit into a 4-6-3 double play.

The Rangers made Eovaldi throw 25 pitches in the fourth, which included a one-out walk to Mazara, leaving him at 55 pitches through four.

Eovaldi, however, seemed to get stronger, mowing down the Rangers in a perfect 13-pitch fifth and striking out two.

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Castro led off the sixth with his third homer of the season, on an 0-and-2 changeup, for a 3-0 lead.