Curtis Granderson and Robinson Cano also went deep for the Yankees, who already have 18 homers through eight games. The Red Sox have allowed 19 in their eight games.
David Robertson (1-0) pitched 1-2-3 perfect innings after starter Ivan Nova was lifted with one out in the fifth with the Yankees leading 7-4. Clay Buchholz (0-2) allowed five runs on eight hits in 3 2/3 innings as Boston's starters continued to struggle.
The Red Sox cut their deficit to 5-4 with three runs in the fourth before Granderson hit a two-run homer in the fifth. Cano and Martin added solo shots in the sixth and seventh.
Cano fell a triple short of hitting for the cycle when he grounded out in the eighth inning, but went 3-for-4 and raised his batting average at Fenway Park to .465 (20-for-43).
The Red Sox began a 10-game homestand Friday with a 9-6 win over the Yankees after going 0-6 on the road, their worst start to a season since 0-8 in 1945.
They reverted to form on Saturday.
The Yankees went ahead 2-0 in the second on an error by shortstop Jed Lowrie, a double by Cano, a run-scoring groundout by Nick Swisher and an RBI double by Eric Chavez, his first hit with New York.
Boston got within 2-1 in the third when Dustin Pedroia doubled, took third on a groundout and scored when Kevin Youkilis grounded to shortstop Derek Jeter. But New York increased that lead to 5-1 before Buchholz retired a batter in the third.
Granderson walked, Chavez doubled and Martin, who signed a $4 million, one-year contract in December as a free agent from the Los Angeles Dodgers, hit a three-run homer. Buchholz left the game after Jeter and Alex Rodriguez singled later in the third.
In eight games, Boston's starters are 1-5 with a 7.41 ERA while allowing 12 homers in 41 innings.
The Red Sox struck back with three runs in the fourth when Jacoby Ellsbury grounded into a run-scoring force play and Pedroia hit a two-run double, but they didn't score again.
The Yankees, meanwhile added two in the fifth off reliever Felix Doubront when Granderson hit his second homer of the season after Swisher doubled. Cano added his second homer and Martin hit his third, both off former Yankee Alfredo Aceves.
Notes
The Yankees have homered in seven of their eight games and have at least two homers in six of them. … Buccholz allowed four solo homers in his other appearance this year, a 5-1 loss at Texas in which he worked 6 1-3 innings. … Jim Calhoun, coach of the NCAA basketball champion Connecticut Huskies, therw out a ceremonial first pitch. … Pedroia had three doubles after getting three hits, including a homer on Friday.