BOSTON -- Last week, as the Boston Red Sox were still churning toward a division championship, David Price observed a difference between this year's conquest of the American League East and last year's.

"We didn't play meaningful baseball games at the end of the year last year," Price said. "You play meaningful baseball games for 160 to 162 games, that keeps everybody on their toes."

And so, as the Red Sox party after clinching back-to-back AL East titles for the first time in franchise history, they should pause to toast an assist from an unlikely source: the New York Yankees.

The Yanks pushed the Sox all season long, winning 11 of 19 head-to-head matchups, and since their last meeting on Sept. 3, New York went 17-7, forcing Boston to keep its foot on the gas right up until the final series of the regular season.

"I think the simple answer to that is, yes, certainly we have paid close attention to how consistently [the Yankees] have won and continue to win. They're a good team. But I like the fact and love the fact that on nights where they've finished their games already and we've had to come back to maintain the spread, we've done it."

Red Sox manager John Farrell

The Yankees gave the Red Sox everything they could handle -- and then some. The Yanks even threw into the hopper a league investigation of Boston's electronic sign-stealing operation, a mini-controversy that resulted in both teams receiving slaps on the wrist in the form of undisclosed fines and seemed more like a nuisance for commissioner Rob Manfred than a full-blown scandal.

And while Red Sox players went out of their way over the past few weeks to deny they were paying much attention to how the Yankees were playing -- "We don't care what the Yankees do," Price said dismissively -- it was also impossible to ignore.

"I think the simple answer to that is, yes, certainly we have paid close attention to how consistently they have won and continue to win," manager John Farrell said. "They're a good team. But I like the fact and love the fact that on nights where they've finished their games already and we've had to come back to maintain the spread, we've done it."

Indeed, the Red Sox have patented the come-from-behind victory in recent weeks. They rallied from a deficit four times on their recently completed 8-1 road trip to Tampa Bay, Baltimore and Cincinnati, and overcame a three-run margin in the first inning Wednesday night against the Toronto Blue Jays. Extra-inning victories have become their signature. The Red Sox are 15-3 in games that have extended beyond regulation, a success rate that made all the difference in a tight division race.

The Red Sox have been in sole possession of first place every day since Aug. 1, but it has been anything but smooth sailing.

• Price, painted as a co-ace alongside Chris Sale, didn't pitch until Memorial Day and missed another seven weeks in the summer with a tear in his left elbow. Throughout the season, Price feuded with the media, and in June he directed an expletive-laced tantrum at broadcaster/Hall of Fame pitcher Dennis Eckersley on the team plane.

• Second baseman Dustin Pedroia was on the disabled list three times, twice because of problems with his surgically repaired left knee.

• Mookie Betts, Xander Bogaerts and Hanley Ramirez had subpar seasons at the plate. In their first year without retired slugger David Ortiz, the Red Sox are last in the American League in home runs and are averaging 4.86 runs per game, fewer than any of the other four AL playoff teams.

• Sale was dominant for much of the season en route to becoming the first AL pitcher to record 300 strikeouts since Pedro Martinez fanned 313 in 1999 – but has alternated one good start with one bad start for the past month.

• Lefty reliever Robbie Ross Jr. and knuckleballer Steven Wright had season-ending surgeries. Tyler Thornburg, acquired last winter to be the primary setup man, never threw a pitch before undergoing surgery for thoracic outlet syndrome.

"If you had painted that scenario, I don't think that's one that we would've felt great about," Red Sox president of baseball operations Dave Dombrowski said. "There are a lot of things that the club has overcome. But you have to tip your cap to guys that have stepped up. Other people have done a really good job. Good leadership helps between John and the coaching staff. But I can't say you would've sat here and said, 'I really love that scenario,' by any means."

Dombrowski bolstered the roster's weak spots by claiming veteran starter Doug Fister off waivers in June, trading for versatile infielder Eduardo Nunez and setup man Addison Reed in July, and adding speedy outfielder Rajai Davis in August. The Red Sox also took the bold step of calling up top prospect Rafael Devers after only 10 days in Triple-A, and the 20-year-old third baseman responded with eight homers and 16 RBIs in his first 77 at-bats.

And the Red Sox were able to play well enough -- and take advantage of a soft part of the schedule -- to go 16-7 since their last game against the Yankees, never allowing their division lead to dip below two games. Unlike last year -- when Boston lost five of the last six regular-season games, coasted into the playoffs, and got swept in the AL Division Series by the Cleveland Indians -- the Sox haven't let up, largely because they couldn't.

It already has led to an AL East title. If it results in a deeper run through October, Boston can give some credit to the Yankees for giving the Sox the push they might have needed to keep them sharp down the stretch.