Now it’s a race.

No, not for first place. The Yankees have a ways to go before that becomes realistic. The battle is within the starting rotation to see who, if anyone, can produce the unimaginable: a complete game.

Nathan Eovaldi came close Saturday against the Red Sox, going eight innings against the team that reached him for six runs and 10 hits in five innings last Sunday at Fenway Park. With Masahiro Tanaka throwing eight innings and CC Sabathia seven earlier in the week, Eovaldi wanted his shot at a baseball rarity in today’s bullpen-dominated game.

“I felt great,’’ Eovaldi said after the 8-2 victory that extended the Yankees’ mini-winning streak to two after a stretch of seven losses in eight games. “I got a quick inning there [in the eighth] and I was hoping I’d go out for the ninth.’’

But he had thrown 107 pitches, and that was it.

“They said it was pitch count,’’ Eovaldi said. “They have their mind made up. [Joe Girardi] asked me how I felt. I said I felt great. But he made the decision.’’

advertisement | advertise on newsday

Girardi never considered sending Eovaldi out for the ninth. “No, I thought he did a really good job,’’ the manager said. “If he gets in a couple of long at-bats . . . We’re going in another five days, we’re in a long run, no.’’

The Yankees have not had a complete game since Tanaka beat Toronto, 4-1, last Aug. 15.

Eovaldi, who is 2-2 with a 4.78 ERA, offered his take on why he can go from dominant to hittable, or vice versa, in the space of one start. “I just feel like a lot of times, it’s just location,’’ he said. “I’ll get ahead of guys and then I’ll leave my off-speed up. I know I don’t really make the adjustments when I need to.

“But today I felt really good mechanically. When I’m feeling good mechanically, I’m able to locate the ball really well.’’

Eovaldi saved a tired bullpen — Dellin Betances and Andrew Miller were unavailable — which further pleased Girardi.

Yankees videos

“For me, the motivation was there just because my last outing against these guys,’’ Eovaldi said of the Red Sox. “I wanted to go out and do better.’’

Eovaldi gave up two earned runs, six hits and no walks in matching his career high for innings pitched in a game. He struck out six and clearly outdueled David Price, who struggled with his control and couldn’t get out of the fifth.

Eovaldi gave up a two-out RBI single by Brock Holt in the second and a home run by Jackie Bradley Jr. in the fifth, but the Yankees already were in the midst of their 11-hit attack.

Austin Romine’s three-hit day started with an RBI double in the third. Didi Gregorius doubled home three runs with two outs in the fourth for a 4-1 lead and Carlos Beltran’s two-out, two- run double made it 6-2 in the fifth. Aaron Hicks added a sacrifice fly in the sixth and Romine had an RBI double in the eighth.

“We haven’t had a lot of offensive explosions,’’ Girardi said. “To get eight runs today was really nice. Everyone contributed, which was even better.’’

advertisement | advertise on newsday

Chase Headley started the day with a .151 average but raised it to .169 with two hits. “It was nice to get a couple of balls to fall in today,’’ the beleaguered third baseman said. “I’m just trying to remember what type of player I’ve been my entire career.’’

Price is 14-7 in his career against the Yankees, but they didn’t bother to look at his stats.

“Sometimes,’’ Beltran said, “it’s just better to go out, see the ball, hit the ball.’’