Price is 1-0 and has not allowed an earned run in two starts this season.
Aaron Judge had three hits for the Yankees, a drive off Sale over the center field wall in the fifth for his third home run of the season.
As the Red Sox and Yankees renewed baseball's best rivalry, Betts put on a performance of a lifetime.
Through the first 10 games Harper leads the league in home runs and is comfortably ahead of the field in drawing walks; incredibly he has hit a home run more often than he has been struck out, highlighting himself as the biggest threat to pitchers in the majors.
Yankees slugger Giancarlo Stanton went 2 for 4. Odubel Herrera also went 2-for-4 with a pair of doubles, an RBI and run for the Phillies.
Luis Severino gave up four runs in the first two innings - five overall.
Granderson's first homer as a Blue Jay occurred after Sanchez (1-1) lost his no-hit bid on the first pitch of the eighth by allowing a double to Tim Beckham.
Boston played its first nine games of the season with nary an error, although Christian Vazquez was charged with a harmless passed ball.
Amber Rose reaches out to Khloe Kardashian after Thompson cheating claims
The woman who was responsible for filming the footage told MailOnline: "They were talking and being around each other all night". The pair were filmed chatting intensely before she appears to lean her head into Tristan's hoodie and puts her arm on his back.
The Yankees brought in Chasen Shreve with two outs in the inning and runners at first and second.
Brock Holt walked and Betts cleared the bases with his shot over the Green Monster to put the Red Sox up 14-1.
Despite losing most of his battles with Sale, he did manage to hit a double in the late stages of the game off Red Sox reliever Brian Johnson - the first extra-base hit for Stanton since April 4.
Yankees: Manager Aaron Boone said he chose to use c Gary Sanchez (right calf) in the DH spot Tuesday as opposed to catcher just as a precaution. We've got two more [games] here. They have started the season by taking four straight series, including this one over the last-place Marlins.
The Red Sox designated hitter is off to a hot start, after proclaiming he was going to hit 30 home runs and steal 30 bases at the start of the season.
"I said, [Darn] it, I'll leave the lineup like it is", Morgan continued.
"He's a work in progress", Cora said, "but we'll take it easy with him".
Angels 11, Rangers 1: Los Angeles (9-3) matched the best start in team history with a road victory over Texas. Reliever Tyler Thornburg (right shoulder surgery) threw on Monday, hitting 95 miles per hour. He'll be in Fort Myers working an extended throwing program and the team will then make a decision at the end of the week. Severino (2-1) saw his ERA jump from 1.38 to 3.50. He is 15-11 with a 4.53 ERA in 38 career appearances (37 starts) against NY.