Mookie Betts also had three RBIs for the Red Sox, who shut out the Yankees at home for the first time since 2011. Boston had not beaten New York by eight or more runs in a shutout at Fenway Park since 1973.
The Red Sox will look to sweep the three-game series Sunday night when new ace David Price gets his first regular-season taste of the longtime rivalry.
Boston isn't just piecing runs together. The Red Sox are scoring in bunches and hitting the ball hard. Bradley also doubled Saturday in addition to his triples.
"I think it just makes for a longer run," Bradley said, joking about his triples. "It's always good. That means you're put in a good place usually when you're able to get triples."
Rick Porcello (5-0) had six strikeouts and gave up five hits in seven innings to tie for the major league lead in wins.
Porcello has pitched at least six innings in each of his last 13 starts since coming off the disabled list last August. That is the longest such streak of his career and the longest active streak in the majors.
"I felt like my sinker was actually a little sporadic the first two innings," Porcello said. "I kind of found a groove with it, settled in."
The Yankees managed five hits. Michael Pineda (1-3) took the loss, allowing two runs and five hits in five innings.
New York has dropped four straight and 12 of 16. In their last four losses, the Yankees have been outscored 25-5. This defeat marked their second four-game skid this season.
The lack of production is not going unnoticed in the locker room.
"It's frustrating," Brett Gardner said. "I feel like we have a good team, a good offensive unit. ... Right now, things obviously are going more wrong than right."
Boston entered the night leading the American League with 5.13 runs per game, and the bats didn't show any signs of slowing down.
Pineda had won his previous three starts at Fenway Park, giving up just one earned run in each victory. That changed in the second inning when Betts dropped in a little flare down the right-field line for a double that scored Christian Vazquez and Bradley.
Boston scored twice in the sixth. Ortiz added the fifth home run of his farewell season -- and second in two nights against the Yankees -- in the seventh, taking Johnny Barbato's fastball over the right-field fence.
"We had a number of good at-bats up and down the lineup," Red Sox manager John Farrell said. "There's not one guy that's looking to be the hero on a given night. It's a unit the way it's functioning right. So we stay with that approach that should pay good dividends."
Yankees: Manager Joe Girardi said OF Aaron Hicks, who pinch-hit in the eighth inning after missing the last six games with left shoulder bursitis, should be ready to return to the starting lineup Sunday.
Red Sox: RHP Carson Smith (right flexor muscle strain) made his first rehab appearance Friday night with Double-A Portland, retiring the only two Reading batters he faced. Smith pitched another clean, nine-pitch inning Saturday. Farrell said Smith will be evaluated Sunday and remains on track to be activated from the DL for Boston's series in Chicago next week.
Yankees closer Aroldis Chapman was back on the mound in Florida one day after announcing on Instagram that he had become a U.S. citizen. The left-hander completed his third week of extended spring training games by striking out two and allowing one hit over a scoreless inning against Pittsburgh minor leaguers. Chapman, serving a 30-game suspension stemming from baseball's new domestic violence policy, can join the Yankees on May 9.
BIG PAPI'S BIG MONTH
Ortiz had his second-best April batting average (minus 2013 when he played just five games because of injury) in 20 big league seasons. He hit .321 with five homers and 19 RBI. His best was 2012 when he batted .405 with six homers and 20 RBI.
WHERE ARE THE RUNS?
The Yankees have been held to three or fewer runs in each of their last seven games, their longest such streak since an eight-game stretch in September 2014.
Yankees: RHP Nathan Eovaldi (1-2, 4.38 ERA) makes his fifth start of the season Sunday night. He took a no-hitter into the seventh inning of his previous outing Monday at Texas.
Red Sox: Price (3-0, 5.76) is 13-7 in his career against the Yankees, with a 4.04 ERA in 31 games. He is 3-0 in his last four starts against them.
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