Boston’s Kiké Hernandez, right, is welcomed to the dugout by Justin Turner after scoring the go-ahead run on a double by Connor Wong in the sixth inning of a doubleheader opener Sunday against the New York Yankees. Steven Senne/Associated Press

BOSTON — It’s too bad baseball went away from unbalanced schedules, because the Boston Red Sox could really use a bunch more games against the New York Yankees.

The Red Sox beat their AL East rivals 4-1 on Sunday night, completing a doubleheader and series sweep that brought them just two games behind their longtime nemeses in the division. Boston won the series opener, 15-5, and then took Sunday’s day game, 6-2, in a makeup of Saturday’s rainout.

“We like playing them. They like playing against us,” Red Sox Manager Alex Cora said. “It’s fun playing against them. Regardless of where we are in the standings, it’s always fun. They have a good team; they’ll be there in the hunt. And we want to be where they were last year.”

The Red Sox (37-35) improved to 5-1 against the Yankees (39-33) this season, with seven more games to play. In the unbalanced schedule that was used until this year, the division rivals played each other 19 times a season.

It’s the first time the Red Sox have swept the Yankees in a doubleheader since 2006, and the first time they did it at Fenway Park since since 1976.

“Sweeping any team is pretty good,” said Red Sox center fielder Jarren Duran, who made a nice catch against the bullpen wall in the night game. “Three games in a row sweeping a really good team like the Yankees – they’re going really good – it’s always good momentum. And I can’t wait to see what we can do on this on this road trip.”

Alex Verdugo had an RBI double in the day game and then took advantage of some Yankees mistakes in the nightcap, scoring on a catcher’s interference to break a fourth-inning tie and then scoring again in the fifth after reaching on a dropped popup.

Brayan Bello (4-4) struck out a career-high eight in the second game, allowing one run on four hits and three walks in seven innings. Kenley Jansen pitched the ninth to earn his 15th save.

Luis Severino (0-2) gave up four runs – three earned – and seven hits with three walks while striking out six.

The night game featured some rare crisp defense by the Red Sox, with Pablo Reyes making two outstanding plays at shortstop. But it also featured a catcher’s interference, a batter’s interference, one pickoff for each team and a caught stealing.

In the day game, Gleyber Torres hit a first-inning, two-run homer for the Yankees, who were without slugger and reigning AL MVP Aaron Judge for the 11th straight game because of a sprained right toe. They are 8-14 when he’s been on the injured list this season.

“That’s the story line,” Yankees Manager Aaron Boone said between games. “We’re going to get beat over the head with that. The reality is: That team we’re rolling out there is capable of doing damage offensively. … That, to me, is just an excuse right now.”

Connor Wong hit an RBI double off the Green Monster against Michael King (1-3) in the day game to give the Red Sox a 3-2 lead. Two pitches later, Verdugo hit another RBI double.

Nick Pivetta (4-4), demoted to the bullpen in mid-May, worked three perfect innings of relief with four strikeouts for the victory.

LOOKING BETTER

Judge visited with fans, signing autographs and taking pictures on the field outside New York’s dugout about 2½ hours before the start. When finished, he said he was heading for some “rehab treatments.” Boone said the slugger “looks better” and “seems to be walking better.”

On Friday, Judge had his second platelet-rich plasma injection on his sprained right toe. “I know he was pretty beat up (Friday). He was in a lot of pain,” Boone said.

DAD MEMORIES

“Just so grateful that I had a dad that took us to work with him all the time,” Yankees Manager Aaron Boone said of his 75-year-old father, Bob, a former MLB catcher. “He came up the end of 1972 and I was born the spring of ’73, and (he) played until my senior year of high school. Literally, I was at the ballpark – my brothers and I – in (uniform) shagging, doing everything you could possibly imagine. A great way to grow up.”

Boone’s bother, Bret, also played in the big leagues, and another brother, Matt, played minor league ball.

TRAINER’S ROOM

Yankees: Boone said outfielder Harrison Bader (strained right hamstring) “should be good to go” and come off the injured list on Tuesday.