Nick Swisher slugged a three-run homer in the first inning, and Jayson Nix also cleared the Green Monster with a solo shot in the fourth inning as the Yankees clubbed back-to-back homers for the fourth and fifth times this season.
"This team is designed to hit home runs, it's kind of our thing," Swisher said. "Everyone talks about hits with runners in scoring position, but if you hit 200 home runs a year as a team, that's going to score you an awful lot of runs."
Making his second start since being reinstated to the rotation, Garcia turned in a stellar outing, utilizing his soft-tossing approach to keep Boston's hitters off balance.
"I feel great today; located the fastball," Garcia said. "I had good velocity today and a good slider. We got the lead early. That's what I need. We made a couple of good plays and made good pitches. It feels great to go out there and win."
The Red Sox did not manage a hit off Garcia until David Ortiz singled in the fourth inning, later coming around to score on a Mauro Gomez single that marked Boston's only run off Garcia.
"We have four games [this weekend] and it's always crazy here," Garcia said. "We have a couple more games to go. Anything can happen. I'm glad I did my job and saved the bullpen."
Garcia threw 100 pitches (62 strikes), scattering six hits to pick up his first victory as a starter this season and third overall. He walked two and struck out five, rebounding from what manager Joe Girardi suspected was an April bout with dead arm.
"I saw signs in the bullpen that he was throwing the ball better," Girardi said. "Freddy was like, 'I'm going to get back.' He was committed to getting back. He did it."
Morales lasted just 3 1/3 innings, running up a high pitch count quickly. Swisher snapped a personal 0-for-17 skid with his long three-run drive over the wall.
"The past three, four days have been a little stressful," Swisher said. "But in a situation like that, I've just got to get back to being more aggressive, looking for some pitches to drive. It's just nice to start the game off like that."
That blast was quickly followed by Jones' drive on a full-count offering, as he took the first step toward his 43rd career multi-homer game.
"I know I didn't hit a home run for a while and I've been battling," Jones said. "Today he made a couple mistakes and I took advantage of them. We were lucky to jump on him early and get Freddy some run support so he could go out there and do his job."
Jones also helped the cause on defense in the sixth inning, leaping against the Monster to snatch Adrian Gonzalez's fly ball and then firing to Robinson Cano, who relayed on to first base to double up Ortiz.
"The double play was good," Jones said. "I thought I had the ball, but I didn't think he was that far around second base. When I saw him, I just threw it right away to Robbie. Robbie made a great play, and [Mark] Teixeira stayed on the bag."
The contest marked the Yankees' first day-night doubleheader of the season, with this being the third straight season the Yankees have played at least one doubleheader against the Red Sox.