The Boston Red Sox enjoyed their first day off since April 14 on Monday, boarding a plane for Chicago and a three-game series against the American League-leading White Sox.

They wrapped up the first month of the season with an impressive sweep of the New York Yankees. Baseball’s most storied rivalry might not be what it was 10 years ago, but there’s no question these two teams still measure themselves against one another. The New Yorkers came to Boston having gone 23-15 against the Sox in the last two seasons, and having made the playoffs in four of the last six seasons.

The Red Sox have been to the playoffs just once in that stretch, a championship run in 2013. Their search for consistency has faltered in the competitive AL East, and their struggles against the Yankees demonstrate those deficiencies.

Friday’s win for the home team at Fenway felt like a page out of 2004. With nothing going on against Masahiro Tanaka, the Sox finally rallied to tie the game with two outs in the seventh inning. It was the end of the night for the Yankees’ ace, and the beginning of a late-inning party at Fenway.

One inning later, David Ortiz delivered the big blow when he drove a Dellin Betances slider into the Monster seats for a winning two-run homer. It was vintage Big Papi, the 48th homer of his career against New York. He hit his 49th a night later. Fifteen of those homers against the Yankees have given the Sox the lead.

As we all know by now, Ortiz is retiring at the end of the season – even though he is having the kind of start to the season that any player of any age would love to have. Retiring 40-year-olds aren’t supposed to have an OPS of 1.051. They’re not supposed to lead the team in doubles and homers. They’re supposed to be fading toward retirement, quietly going into the autumn of their careers.

Ortiz doesn’t do things quietly. Never has. He’s still as big as the bling the team gave out to fans this month, a garish “500” necklace decked out with faux diamonds.

Papi is the only Sox player still around from the 2004 team that staged the “greatest comeback in history” (as inscribed on the sides of its championship ring) against the Yankees. He is the only player alive to have won three World Series rings with Boston. He is a throwback to the days when the rivalry was the biggest thing in all of sports.

Alex Rodriguez is the lone Yankee remaining from that ALCS collapse. He hit a home run on Friday night as well, and another on Sunday. He’s part of a Yankees team that has lost 13 of its last 17 games and is near the bottom of the American League in pitching and hitting.

Rivalries heat up and cool off over time. From 1998 to 2005 the Yankees and Red Sox finished first and second – in that order – every year. When you’re battling for first place year after year, it’s easy to get tired of one another.

That hasn’t been the case of late. The Sox have finished dead last in three of the last four seasons. The Yankees left Boston on Sunday night in last place.

That might not be good news for the rivalry, but it was good news for the Red Sox. Their goal is to win the division, not just the 19 games against New York.

Tom Caron is a studio host for the Red Sox broadcast on NESN. His column appears in the Portland Press Herald on Tuesdays.