Together, they gave the Yankees a big start in the rare five-game series, keying a 12-4 victory over Boston in the opener of Friday's day-night doubleheader.
Damon started things off with a triple, adding a homer and four RBI to help New York move 2½ games up in the AL East.
"I think that's what we've seen on the other side of the field for so many years," New York manager Joe Torre said of Damon, who helped Boston win the 2004 World Series. "He just seems to rise to the occasion. ... We're glad he's on our side; let's put it that way."
Facing their top rivals a day after losing 12-2, the Yankees also got a boost from Abreu, who was acquired from the Phillies at the trade deadline and experienced the craziness for the first time. He had four of the Yankees' 17 hits.
"He's a good player, and he's in the middle of a pennant race," said Boston manager Terry Francona, who had Abreu with the Phillies. "So I'm sure that added to his excitement."
Eric Hinske, playing his first game since being traded from Toronto, and Mark Loretta each hit three doubles for the Red Sox. Boston had nine extra-base hits but finished 0-for-16 with runners in scoring position and lost for the eighth time in 12 games.
"You don't win without timely hits," said Hinske, who received a standing ovation at each at-bat and often when he took the field. "I've never been a part of anything like that."
Manny Ramirez added a home run for Boston.
A May 2 rainout forced the long series. The Yankees and Boston last played a five-game set in 1973 in New York; the last time they did it at Fenway was 1959.
Chien-Ming Wang (14-5) allowed three runs on seven hits and four walks, including two intentional walks to Ramirez. He struck out two and left with an 8-3 lead after Loretta doubled to start the seventh.
Johnson gave up four runs on seven hits and two walks and left in the fifth when Damon hit a two-run homer and Derek Jeter singled and scored.
"It kind of got the crowd quiet again," Damon said of his homer. "I just know what the job at hand is: To get on base, make things happen and win a ballgame."
New York sent nine batters to the plate in the seventh to add four runs and take an 8-3 lead.
Damon, who was a triple short of the cycle Thursday, got the Yankees off to a fast start when he led off the game with a drive over Coco Crisp in center field. The ball rolled into the triangle-shaped warning track for a triple, and Jeter followed with an RBI single.
Damon also made a sliding catch on Alex Gonzalez's sacrifice fly in the sixth with runners at second and third and New York leading 4-2.
Ramirez hit his 33rd home run. Hinske matched a career-high with three doubles but also misplayed a fly ball to right in the ninth.
A logo for the Jimmy Fund was added to the Green Monster in honor of the cancer charity's annual telethon. ... Yankees infielder Andy Phillips went on the 15-day DL with a strained left rib cage muscle. Right-hander T.J. Beam was recalled from Triple-A Columbus. ... Yankees DH Jason Giambi scored his 1,000th career run in the seventh. ... Third baseman Mike Lowell made a nice catch falling into the Yankees' dugout in the second, but in the seventh he missed a slow liner to end his 70-game errorless streak.