Devers hit a stunning homer off Aroldis Chapman to tie the game in the ninth inning, and Benintendi singled home the go-ahead run in the 10th as Boston beat the New York Yankees 3-2 on Sunday night.
"No pressure at all," veteran teammate Hanley Ramirez said. "I think they know what the big leagues are about."
Chris Sale struck out 12 in his latest dominant performance, but Boston trailed 2-1 before the 20-year-old Devers connected on a 103 mph fastball and became the second left-handed hitter to homer off Chapman in his eight-year career.
"An incredible swing," Red Sox manager John Farrell said. "He doesn't fear the moment. He's jumped feet first into this rivalry. It couldn't have come at a better time."
By winning a battle of hard-throwing bullpens, the Red Sox upped their AL East lead to a season-high 5 1/2 games over rival New York. Boston (67-50) took two of three in the series and is a season-best 17 games over .500 after winning 10 of its past 11.
"This is what we live for," Sale said. "A little bit more fun being at Yankee Stadium, where it's enemy territory."
Boston Red Sox
The teams meet again next weekend at Fenway Park. But first, the scuffling Yankees face the crosstown-rival New York Mets in the Subway Series beginning Monday night.
With one out in the 10th, Chapman (4-2) plunked Jackie Bradley Jr. with a 101 mph pitch and walked Eduardo Nunez. Tommy Kahnle walked Mookie Betts before the 23-year-old Benintendi, who had a pair of three-run homers in Saturday's victory, singled to right field.
Todd Frazier gave the Yankees a 2-1 lead in the eighth with a bases-loaded sacrifice fly off Matt Barnes. Chapman entered throwing smoke in the ninth, but couldn't close it out.
Devers, playing his 15th major league game after entering as a pinch hitter in the sixth, drove a 1-2 fastball the other way into the Red Sox bullpen in left-center. He clapped his hands as he rounded first on his fourth home run, which handed Chapman his fourth blown save in 19 chances.
"It was a good pitch," Chapman said through a translator, acknowledging he was a little surprised to see Devers take him deep.
The left-hander was lifted in the 10th and walked off the mound to boos.
"I treat every pitcher the same," Devers said through a translator. "I felt more emotion rounding the bases knowing that I had tied the game."
The only other left-handed hitter to homer off Chapman was Luke Scott for Baltimore in 2011 against Cincinnati.
"It's not easy to stay in there with a guy throwing 103. So, it just kind of shows you the player that he is," Benintendi said about Devers.
Sale went seven innings and increased his major league-leading strikeout total to 241. He allowed four hits and one run - which could have been prevented by better defense.
The AL ERA leader has 16 double-digit strikeout games this season, three versus New York.
Each No. 9 batter had a two-out RBI in the fifth. Bradley put Boston ahead with a single before Austin Romine answered with his first career triple, a drive that glanced off the mitt of Betts, a 2016 Gold Glove winner, as he backed into the right-field wall.
"It's a frustrating loss, there's no doubt about it," Yankees manager Joe Girardi said .
Cool and clear-headed, New York rookie Jordan Montgomery matched Sale for 5 1/3 innings and left to a warm hand from a sellout crowd of 46,610 that included actor Leonardo DiCaprio, who was wearing a Yankees cap. The day before, Montgomery was hit on the head by a fly ball while signing autographs as the Red Sox took batting practice. He bled from a cut on his ear, but was OK to pitch Sunday.
Red Sox: LHP David Price (elbow inflammation) threw from 90 feet. He is scheduled for a day off Monday before resuming his throwing program Tuesday. ... RHP Carson Smith (elbow) tossed a scoreless inning with two strikeouts Saturday in his third rehab outing, second for Triple-A Pawtucket. Farrell said the "early phase" of Smith's rehab assignment has been encouraging, but the reliever is expected to remain in the minors for several weeks. Smith is recovering from Tommy John surgery in May 2016.
Yankees: 1B Greg Bird (right ankle surgery) is scheduled to work out with the team Tuesday and begin a minor league rehab assignment Wednesday. ... All-Star 2B Starlin Castro (strained right hamstring) plans to work out with the club Thursday and start a rehab assignment Friday. ... DH Matt Holliday (back) was slated to take batting practice.
Red Sox: RHP Doug Fister (2-5, 5.03 ERA) faces AL Central-leading Cleveland at Fenway Park on Monday night in the makeup of an Aug. 2 rainout. Trevor Bauer (10-8, 4.79 ERA) pitches for former Red Sox manager Terry Francona and the Indians.
Yankees: Host the depleted Mets (53-62) in the first of two games in the Bronx, followed by a pair at Citi Field. Ex-Mets farmhand Luis Cessa (0-3) will be recalled from the minors to start the opener in place of injured Masahiro Tanaka. Rafael Montero (1-8) pitches for the Mets.