Christian Vazquez will probably have a long and prosperous career in the major leagues because of his soft hands and strong right arm. His skills as a catcher are something special.

If Vazquez can get on base once or twice a game, so much the better. But it’s not something the Red Sox count on at this stage of his development.

That’s what made his swing Sunday night so memorable.

Vazquez hit a home run that was last seen flying over Lansdowne Street, his two-run blast off fearsome Dellin Betances the difference as the Red Sox beat the Yankees, 8-7, to finish a three-game sweep of their rivals.

Was that the best Vazquez had ever hit a ball?

“The farthest, yeah,’’ he said with a little grin. “Great moment.’’

At 15-10, the Red Sox are five games over .500 for the first time since the end of the 2013 season. They have won seven of eight games to move into first place in the American League East. It was their first series sweep of the Yankees since September 2013.

The Sox start a six-game road trip in Chicago on Tuesday night against the White Sox.

The last-place Yankees have lost five straight to fall to 8-15.

On Friday night, David Ortiz guessed that Betances would throw him a curveball and hit the first pitch he saw for a game-winning two-run homer in the eighth inning.

In the seventh inning Sunday, Betances came into a 6-6 game with Brock Holt on first. This time, Betances went with a 97-mile-per-hour fastball right down the middle. Vazquez was ready and launched it over everything for the second home run of his career.

As Betances warmed up, Vazquez had time to confer with hitting coach Chili Davis.

“I was trying to get the fastball and I got it,’’ Vazquez said.

Vazquez had his right arm in a cast a year ago as he recovered from Tommy John surgery. He worked his way back, came off the disabled list April 15 and has been a key contributor since.

“As much as the crowd erupted, so did the dugout,’’ manager John Farrell said. “What great is the way our young guys continue to grow. Tonight Vasky’s the guy.’’

In Vazquez, Ortiz sees a player who can develop much like St. Louis All-Star Yadier Molina did and become an adept hitter.

“He’s been working extremely hard,’’ Ortiz said. “Trust me, I believe the same thing that happened with Yadier is going to happen to him because he works extremely hard on his hitting. He doesn’t just work on his defense. At some point I won’t be surprised if he figures it out.’’

Red Sox starter David Price allowed six runs but improved to 4-0. Craig Kimbrel finished the Yankees off for his eighth save before a non-sellout crowd of 34,279.

The game was played with rain falling throughout, particularly heavy in the early innings, but the teams combined for 23 hits.

The Red Sox twice gave Price leads he could not hold.

Mookie Betts singled to lead off the bottom of the first inning against Nathan Eovaldi, took second on a single, and scored on a fielder’s choice.

Jacoby Ellsbury doubled in a run in the third inning. With two outs, Alex Rodriguez unloaded on a fastball and ball landed in the Monster Seats between the light tower and flagpole.

It was Rodriguez’s fifth home run of the season, the second in the series.

The Red Sox came back with three runs in the bottom of the inning to take the lead again.

Dustin Pedroia and Xander Bogaerts singled before Ortiz drew a five-pitch walk to load the bases. Hanley Ramirez grounded a single up the middle and two runs scored.

With two outs, Holt singled to center field and Ortiz scored a split-second before Ramirez was thrown out going to third. The Yankees challenged the play but the call was confirmed.

Price gave up three more runs in the fifth. He hit Ellsbury with a pitch then walked Brett Gardner on four pitches, two events that defined his overall lack of fastball command. This time Rodriguez belted a two-run double off the wall in center.

Mark Teixeira followed with an RBI single.

The Sox tied the game in the bottom of the inning. With Ramirez on first, Travis Shaw drilled a first-pitch curveball deep into the right field seats for his third home run.

Shaw has struck out in his first two at-bats. But when Eovaldi started with him with a curveball again, he was waiting on it.

“The first two times, I had no chance. I wasn’t seeing anything,’’ Shaw said. “I hoped he would do it again and he did.’’

Said Farrell “Tonight’s a pretty telltale sign of the character of this team. We kept coming offensively.’’

Eovaldi, who had taken a no-hitter into the seventh inning of previous start, allowed six runs on 10 hits over six innings.

Price retired the final eight batters he faced to keep the game tied. When Rodriguez came to the plate in the seventh inning, Farrell went to the mound for a chat and decided to leave Price in the game

“Just wanted to check with him,’’ Farrell said. “In that spot wanted to give him a chance to win.’’

Rodriguez grounded out.

“I appreciate him leaving me out there in that situation, a guy that’s hit the ball against me well twice that night.’’ Price said. “So it was good.’’

Price has allowed five or more earned runs in three of his six starts this season. That happened twice all of 2015.

The $217 million lefthander also has pitched poorly at Fenway Park. Over four starts and 22? innings, Price has allowed 21 earned runs on 27 hits. His earned run average on the season is 6.14.

Peter Abraham can be reached at pabraham@globe.com. Follow him on Twitter @PeteAbe.