Betts hit his major league-leading 16th homer, Sale struck out nine in 7 2/3 innings and the Red Sox beat the Tampa Bay Rays 4-2 on Tuesday night.
"I knew once we got a lead with that guy, we were in pretty good shape," Betts said.
Betts had two hits in four at-bats and is hitting .368.
"He's the best player in the league, I don't think there's any argument on that," Sale said. "It seems like he's hitting a homer every other day. You're in awe of him, the way he handles himself and the work he puts in. He's not just showing up and going out there and doing that."
Boston is 21-9 against the AL East, winning eight of 11 against Tampa Bay.
Willy Adames made his big league debut and hit a solo home run off Sale in his second at-bat. The 22-year-old shortstop went 1 for 4 with three strikeouts. He was acquired from Detroit as part of a three-team trade that sent Rays ace -- and current Sale teammate -- David Price to the Tigers on July 31, 2014.
"You hit a bomb against Sale, it's an amazing feeling," said Adames, who arrived at the ballpark about 40 minutes before first pitch. "I can't tell you how happy I am right now."
Adames is the first player to homer at Tropicana Field in first big league game.
Sale (5-1) gave up four hits and walked two. He has allowed three runs or fewer in his first 11 starts, the longest stretch by a Boston pitcher to open a season since Pedro Martinez's 12 in 2001.
"He's really tough, no doubt," Rays manager Kevin Cash said.
Joe Kelly finished the eighth, and Craig Kimbrel got into a bases-loaded jam before getting his 14th save in 16 chances when Mallex Smith grounded into a game-ending forceout on his 32nd pitch of the ninth. Jesus Sucre led off with a single, pinch-hitter Brad Miller doubled with two outs and Rob Refsynder walked.
Betts hit a go-ahead, three-run drive in the third off Jake Faria (3-3), who left two batters later because of a strained left oblique. Faria was replaced with a 1-2 count on Hanley Ramirez by Austin Pruitt, who gave up one run in 5 1/3 innings.
Cash said Faria "is going to miss some time."
Ramos said the hand "sore" but didn't rule out being available Wednesday.
Faria allowed three runs and three hits in 2 2/3 innings.
The announced attendance was 10,642, below the Rays' AL-low home average of 14,711. Miami is last in the majors at 10,603.
Red Sox: Asked whether 2B Dustin Pedroia (left knee surgery) could return Friday against Atlanta, manager Alex Cora said "it depends on how he reacts but he's getting close." Pedroia is on a rehab assignment with Triple-A Pawtucket. ... RHP Hector Velazquez (lower back strain) could be back later this week.
Rays: RHP Nathan Eovaldi (right elbow surgery) could make his final rehab start Wednesday night for Triple-A Durham.
Betts has scored a major-league best 49 runs. He has 36 extra-base hits, including six over his last four games.
Price (4-4), coming off a complete game victory over Baltimore, goes against Rays RHP Chris Archer (3-3) on Wednesday night. "There will be a little bit of banter, but it's all friendly," Archer said.
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