FORT MYERS — David Price got his first taste of what the Red Sox-Yankees rivalry is all about last night, and it tasted good.

Fans jammed JetBlue Park to boo A-Rod, hoot the Yankees, glory in the dress white uniforms worn by the Olde Town Team and root for victory, meaningless though it might be. The only thing missing were the Yankees.

Oh, Alex Rodriguez was in the lineup, and so was Mark Teixeira, but who the heck is Slade Heathcott or Pete Kozma? Are we really going to learn how to hate Austin Romine and Chris Denorfia? Well, as long as they’re wearing blue shirts with NEW YORK across the front in pearly white, yes we are.

Price could have missed last night’s affair and thrown a simulated game early in the day, getting home in time for dinner and maybe even a round of golf, but he opted to face the Yankees, a decision manager John Farrell explained by saying, “The priority is getting David ready.” The guess is for what?

Whether he meant for the season or for the Yankees was unclear, but he did both last night, giving up three hits and a home run but otherwise making the two Yankees who were really Yankees — Rodriguez and Teixeira — look silly. He struck A-Rod out twice, the second time leaving him looking at a pitch so nasty Rodriguez just stared at it in the glove of catcher Ryan Hanigan for a long second and then whirled and walked back to the dugout, a beaten batter.

He did the same to Teixeira in the first inning with a pitch that left him stuck between should I or shouldn’t I, baseball’s no-man’s land. Price did not pump his fist about any of this or make any other disparaging gestures, which frankly most of the crowd would have loved had he chosen to do so.

Instead he just continued to make clear to those in attendance that he is who we thought he was when the Sox signed him to a seven-year, $217 million deal in early December, while making equally clear to his new teammates that he is one of them, even on a night when he could have avoided the late shift if he wanted to but instinctively understood the place to be in Fort Myers was on the mound facing the imitation Yankees.

“I take the same attitude, the same mindset, if I’m pitching on a back field against a High A (team),” Price said. “What’s on the front of the jersey or the name on the back doesn’t concern me.

“I don’t really care who I’m facing. I don’t look at whose on deck. If I execute my game, I feel I can record outs.”

Having said that, Price quickly added that while this was a meaningless moment in March, he well understood already that the name on the front of those blue jerseys meant something even if the ones on the back of most of them didn’t.

“It’ll be intense,” Price said of facing the real Yankees while wearing red Sox. “It’s the biggest rivalry I’ve been a part of. It’ll be 18, 19 games of good baseball. I’m looking forward to that.”

If he pitches those games the way he did last night’s, the Yankees won’t, but his new teammates and all of Red Sox Nation will. At this early stage of things, how his new teammates view him is as important as getting out a bunch of faux Yankees in a spring training game, and by all accounts, he’s been as successful at that as he was in his four-inning stint last night.

“The personal relationships in the clubhouse, that’s happening by the day,” Farrell said of Price before the game. “You hear guys who have been here a couple of years that talk about his genuineness, his willingness to watch, listen and give feedback, whether it’s something in between the lines during the game or something in the clubhouse.

“His reputation precedes him, and we’re seeing that in the person he is. I think with the attention given because of the free agent signing, that doesn’t take away from his work. I think he’s very comfortable being the guy, being a No. 1 starter, and all that comes with it, and he’s handled that in stride.”

Certainly he handled the Yankees, such as they were. Manhandled them, really. Sure Aaron Hicks took him deep to right-center field in the third inning, but other than that, Price struck out six of the 15 batters he faced, five of them looking, and was in clear command of the situation.

Every one of those guys who struck out looking — from A-Rod to Romine, from Denorfia to Teixeira to Kozma — wore the same look on their face after Price broke off a pitch that had left them helpless and swingless.

“What in the world was that?” they seemed to say.

What that was, was the guy all Boston hopes David Price will be this summer and for many more.